diff --git a/NEWS.md b/NEWS.md
index 8ac937cee0..f01f12598c 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -17,6 +17,7 @@
 * [Data.Iris](https://github.com/FluxML/Flux.jl/pull/652) makes Fisher's Iris dataset available with `Iris.labels` and `Iris.features`.
 * New [InstanceNorm](https://github.com/FluxML/Flux.jl/pull/634), as popularized by [Instance Normalization: The Missing Ingredient for Fast Stylization](https://arxiv.org/abs/1607.08022).
 * New [GroupNorm](https://github.com/FluxML/Flux.jl/pull/696), as described in [Group Normalization](https://arxiv.org/abs/1803.08494).
+* New [CrossCor](https://github.com/FluxML/Flux.jl/pull/762).
 
 AD Changes:
 
diff --git a/docs/src/models/layers.md b/docs/src/models/layers.md
index ec45c31e7b..3acb910ddb 100644
--- a/docs/src/models/layers.md
+++ b/docs/src/models/layers.md
@@ -17,6 +17,7 @@ MaxPool
 MeanPool
 DepthwiseConv
 ConvTranspose
+CrossCor
 ```
 
 ## Recurrent Layers
diff --git a/src/Flux.jl b/src/Flux.jl
index eccdd6a7e5..a041a69a8d 100644
--- a/src/Flux.jl
+++ b/src/Flux.jl
@@ -6,7 +6,7 @@ using Base: tail
 using MacroTools, Juno, Requires, Reexport, Statistics, Random
 using MacroTools: @forward
 
-export Chain, Dense, Maxout, RNN, LSTM, GRU, Conv, ConvTranspose, MaxPool, MeanPool,
+export Chain, Dense, Maxout, RNN, LSTM, GRU, Conv, CrossCor, ConvTranspose, MaxPool, MeanPool,
        DepthwiseConv, Dropout, AlphaDropout, LayerNorm, BatchNorm, InstanceNorm, GroupNorm, 
        params, mapleaves, cpu, gpu, f32, f64
 
diff --git a/src/layers/conv.jl b/src/layers/conv.jl
index 3739fd1c34..ff547b410b 100644
--- a/src/layers/conv.jl
+++ b/src/layers/conv.jl
@@ -198,6 +198,76 @@ end
 
 (a::DepthwiseConv{<:Any,<:Any,W})(x::AbstractArray{<:Real}) where {T <: Union{Float32,Float64}, W <: AbstractArray{T}} =
   a(T.(x))
+"""
+    CrossCor(size, in=>out)
+    CrossCor(size, in=>out, relu)
+  
+Standard cross convolutional layer. `size` should be a tuple like `(2, 2)`.
+`in` and `out` specify the number of input and output channels respectively.
+    
+Example: Applying CrossCor layer to a 1-channel input using a 2x2 window size,
+         giving us a 16-channel output. Output is activated with ReLU.
+    
+    size = (2,2)
+    in = 1
+    out = 16 
+    CrossCor((2, 2), 1=>16, relu)
+    
+Data should be stored in WHCN order (width, height, # channels, # batches). 
+In other words, a 100×100 RGB image would be a `100×100×3×1` array, 
+and a batch of 50 would be a `100×100×3×50` array.
+    
+Takes the keyword arguments `pad`, `stride` and `dilation`.
+"""
+struct CrossCor{N,M,F,A,V}
+  σ::F
+  weight::A
+  bias::V
+  stride::NTuple{N,Int}
+  pad::NTuple{M,Int}
+  dilation::NTuple{N,Int}
+end
+
+function CrossCor(w::AbstractArray{T,N}, b::AbstractVector{T}, σ = identity;
+              stride = 1, pad = 0, dilation = 1) where {T,N}
+  stride = expand(Val(N-2), stride)
+  pad = expand(Val(2*(N-2)), pad)
+  dilation = expand(Val(N-2), dilation)
+  return CrossCor(σ, w, b, stride, pad, dilation)
+end
+
+CrossCor(k::NTuple{N,Integer}, ch::Pair{<:Integer,<:Integer}, σ = identity;
+     init = glorot_uniform, stride = 1, pad = 0, dilation = 1) where N =
+  CrossCor(param(init(k..., ch...)), param(zeros(ch[2])), σ,
+       stride = stride, pad = pad, dilation = dilation)
+
+@treelike CrossCor
+
+function crosscor(x, w, ddims::DenseConvDims)
+  ddims = DenseConvDims(ddims, F=true)
+  return conv(x, w, ddims)
+end
+
+function (c::CrossCor)(x::AbstractArray)
+  # TODO: breaks gpu broadcast :(
+  # ndims(x) == ndims(c.weight)-1 && return squeezebatch(c(reshape(x, size(x)..., 1)))
+  σ, b = c.σ, reshape(c.bias, map(_->1, c.stride)..., :, 1)
+  cdims = DenseConvDims(x, c.weight; stride=c.stride, padding=c.pad, dilation=c.dilation)
+  σ.(crosscor(x, c.weight, cdims) .+ b)
+end
+
+function Base.show(io::IO, l::CrossCor)
+  print(io, "CrossCor(", size(l.weight)[1:ndims(l.weight)-2])
+  print(io, ", ", size(l.weight, ndims(l.weight)-1), "=>", size(l.weight, ndims(l.weight)))
+  l.σ == identity || print(io, ", ", l.σ)
+  print(io, ")")
+end
+
+(a::CrossCor{<:Any,<:Any,W})(x::AbstractArray{T}) where {T <: Union{Float32,Float64}, W <: AbstractArray{T}} =
+  invoke(a, Tuple{AbstractArray}, x)
+
+(a::CrossCor{<:Any,<:Any,W})(x::AbstractArray{<:Real}) where {T <: Union{Float32,Float64}, W <: AbstractArray{T}} =
+  a(T.(x))
 
 """
     MaxPool(k)
diff --git a/test/cuda/cuda.jl b/test/cuda/cuda.jl
index 86e7f2f3b8..96d04c284b 100644
--- a/test/cuda/cuda.jl
+++ b/test/cuda/cuda.jl
@@ -36,6 +36,10 @@ c = gpu(Conv((2,2),3=>4))
 l = c(gpu(rand(10,10,3,2)))
 Flux.back!(sum(l))
 
+c = gpu(CrossCor((2,2),3=>4))
+l = c(gpu(rand(10,10,3,2)))
+Flux.back!(sum(l))
+
 end
 
 @testset "onecold gpu" begin
diff --git a/test/layers/conv.jl b/test/layers/conv.jl
index 5e12e42668..5b2e2392ca 100644
--- a/test/layers/conv.jl
+++ b/test/layers/conv.jl
@@ -56,6 +56,27 @@ end
   @test size(x_hat) == size(x)
 end
 
+@testset "CrossCor" begin
+  x = rand(Float32, 28, 28, 1, 1)
+  w = rand(2,2,1,1)
+  y = CrossCor(w, [0.0])
+
+  @test sum(w .* x[1:2, 1:2, :, :]) == y(x)[1, 1, 1, 1]
+  
+  r = zeros(Float32, 28, 28, 1, 5)
+  m = Chain(
+    CrossCor((2, 2), 1=>16, relu),
+    MaxPool((2,2)),
+    CrossCor((2, 2), 16=>8, relu),
+    MaxPool((2,2)),
+    x -> reshape(x, :, size(x, 4)),
+    Dense(288, 10), softmax)
+
+  @test size(m(r)) == (10, 5)
+  @test y(x) != Conv(w, [0.0])(x)
+  @test CrossCor(w[end:-1:1, end:-1:1, :, :], [0.0])(x) == Conv(w, [0.0])(x)
+end
+
 @testset "Conv with non quadratic window #700" begin
   data = zeros(Float32, 7,7,1,1)
   data[4,4,1,1] = 1
@@ -81,3 +102,4 @@ end
     true
   end
 end
+