diff --git a/src/acorn/parser/class-fields.js b/src/acorn/parser/class-fields.js
index 0d1b13b7a..759cac777 100644
--- a/src/acorn/parser/class-fields.js
+++ b/src/acorn/parser/class-fields.js
@@ -35,17 +35,20 @@ function init() {
   }
 
   function parseClassElement(func, args) {
-    if (this.type !== tt.name) {
+    const { type } = this
+
+    if (type !== tt.bracketL &&
+        type !== tt.name) {
       return Reflect.apply(func, this, args)
     }
 
-    const { type } = lookahead(this)
+    const nextType = lookahead(this).type
 
-    if (type === tt.parenL ||
-        type === tt.star ||
-        (type !== tt.braceR &&
-         type !== tt.eq &&
-         type !== tt.semi &&
+    if (nextType === tt.parenL ||
+        nextType === tt.star ||
+        (nextType !== tt.braceR &&
+         nextType !== tt.eq &&
+         nextType !== tt.semi &&
          (this.isContextual("async") ||
           this.isContextual("get") ||
           this.isContextual("set") ||
@@ -55,8 +58,7 @@ function init() {
 
     const node = this.startNode()
 
-    node.computed = false
-    node.key = this.parseIdent(true)
+    this.parsePropertyName(node)
 
     node.value = this.eat(tt.eq)
       ? this.parseExpression()
diff --git a/test/compiler-tests.mjs b/test/compiler-tests.mjs
index b01272a77..9e85ec83f 100644
--- a/test/compiler-tests.mjs
+++ b/test/compiler-tests.mjs
@@ -394,18 +394,20 @@ describe("compiler tests", () => {
     const code = [
       "export class A { a }",
       'export class B { b = "b" }',
-      "export class C { #c }",
-      "export class D { async }",
-      "export class E { get }",
-      "export class F { set }",
-      "export class G { static }",
-      "export class H {",
-      '  #h= "h"',
-      "  h() {",
-      "    return this.#h",
+      "export class C { [c] }",
+      'export class D { [d] = "d" }',
+      "export class E { #e }",
+      "export class F { async }",
+      "export class G { get }",
+      "export class H { set }",
+      "export class I { static }",
+      "export class J {",
+      '  #j= "j"',
+      "  j() {",
+      "    return this.#j",
       "  }",
       "}",
-      "export class I {",
+      "export class K {",
       "  async = 1;",
       "  get = 1",
       "  set = 1",