diff --git a/expression/builtin_math.go b/expression/builtin_math.go
index 919097489e59e..ad2c0b87d7822 100644
--- a/expression/builtin_math.go
+++ b/expression/builtin_math.go
@@ -943,9 +943,23 @@ func (c *randFunctionClass) getFunction(ctx sessionctx.Context, args []Expressio
 	bf := newBaseBuiltinFuncWithTp(ctx, args, types.ETReal, argTps...)
 	bt := bf
 	if len(args) == 0 {
-		sig = &builtinRandSig{bt, nil}
+		seed := time.Now().UnixNano()
+		sig = &builtinRandSig{bt, rand.New(rand.NewSource(seed))}
+	} else if _, isConstant := args[0].(*Constant); isConstant {
+		// According to MySQL manual:
+		// If an integer argument N is specified, it is used as the seed value:
+		// With a constant initializer argument, the seed is initialized once
+		// when the statement is prepared, prior to execution.
+		seed, isNull, err := args[0].EvalInt(ctx, nil)
+		if err != nil {
+			return nil, err
+		}
+		if isNull {
+			seed = time.Now().UnixNano()
+		}
+		sig = &builtinRandSig{bt, rand.New(rand.NewSource(seed))}
 	} else {
-		sig = &builtinRandWithSeedSig{bt, nil}
+		sig = &builtinRandWithSeedSig{bt}
 	}
 	return sig, nil
 }
@@ -964,21 +978,11 @@ func (b *builtinRandSig) Clone() builtinFunc {
 // evalReal evals RAND().
 // See https://dev.mysql.com/doc/refman/5.7/en/mathematical-functions.html#function_rand
 func (b *builtinRandSig) evalReal(row types.Row) (float64, bool, error) {
-	if b.randGen == nil {
-		b.randGen = rand.New(rand.NewSource(time.Now().UnixNano()))
-	}
 	return b.randGen.Float64(), false, nil
 }
 
 type builtinRandWithSeedSig struct {
 	baseBuiltinFunc
-	randGen *rand.Rand
-}
-
-func (b *builtinRandWithSeedSig) Clone() builtinFunc {
-	newSig := &builtinRandWithSeedSig{randGen: b.randGen}
-	newSig.cloneFrom(&b.baseBuiltinFunc)
-	return newSig
 }
 
 // evalReal evals RAND(N).
@@ -988,15 +992,22 @@ func (b *builtinRandWithSeedSig) evalReal(row types.Row) (float64, bool, error)
 	if err != nil {
 		return 0, true, errors.Trace(err)
 	}
-	if b.randGen == nil {
-		if isNull {
-			// When seed is NULL, it is equal to RAND().
-			b.randGen = rand.New(rand.NewSource(time.Now().UnixNano()))
-		} else {
-			b.randGen = rand.New(rand.NewSource(seed))
-		}
+	// b.args[0] is promised to be a non-constant(such as a column name) in
+	// builtinRandWithSeedSig, the seed is initialized with the value for each
+	// invocation of RAND().
+	var randGen *rand.Rand
+	if isNull {
+		randGen = rand.New(rand.NewSource(time.Now().UnixNano()))
+	} else {
+		randGen = rand.New(rand.NewSource(seed))
 	}
-	return b.randGen.Float64(), false, nil
+	return randGen.Float64(), false, nil
+}
+
+func (b *builtinRandWithSeedSig) Clone() builtinFunc {
+	newSig := &builtinRandWithSeedSig{}
+	newSig.cloneFrom(&b.baseBuiltinFunc)
+	return newSig
 }
 
 type powFunctionClass struct {
diff --git a/expression/integration_test.go b/expression/integration_test.go
index 2bcb10f3862da..5cfd35f85772c 100644
--- a/expression/integration_test.go
+++ b/expression/integration_test.go
@@ -542,6 +542,13 @@ func (s *testIntegrationSuite) TestMathBuiltin(c *C) {
 	// for radians
 	result = tk.MustQuery("SELECT radians(1.0), radians(pi()), radians(pi()/2), radians(180), radians(1.009);")
 	result.Check(testkit.Rows("0.017453292519943295 0.05483113556160754 0.02741556778080377 3.141592653589793 0.01761037215262278"))
+
+	// for rand
+	tk.MustExec("drop table if exists t")
+	tk.MustExec("create table t(a int)")
+	tk.MustExec("insert into t values(1),(2),(3)")
+	tk.MustQuery("select rand(a) from t").Check(testkit.Rows("0.6046602879796196", "0.16729663442585624", "0.7199826688373036"))
+	tk.MustQuery("select rand(1), rand(2), rand(3)").Check(testkit.Rows("0.6046602879796196 0.16729663442585624 0.7199826688373036"))
 }
 
 func (s *testIntegrationSuite) TestStringBuiltin(c *C) {