diff --git a/‎packages/eslint-plugin/src/rules/prefer-literal-enum-member.ts
Lines changed: 18 additions & 7 deletions b/‎packages/eslint-plugin/src/rules/prefer-literal-enum-member.ts
Lines changed: 18 additions & 7 deletions
diff --git a/‎packages/eslint-plugin/tests/rules/prefer-literal-enum-member.test.ts
Lines changed: 48 additions & 0 deletions b/‎packages/eslint-plugin/tests/rules/prefer-literal-enum-member.test.ts
Lines changed: 48 additions & 0 deletions
@@ -1,7 +1,7 @@
 import { AST_NODE_TYPES } from '@typescript-eslint/experimental-utils';
 import { createRule } from '../util';
 
-export default createRule<[], 'notLiteral'>({
+export default createRule({
   name: 'prefer-literal-enum-member',
   meta: {
     type: 'suggestion',
@@ -22,15 +22,26 @@ export default createRule<[], 'notLiteral'>({
     return {
       TSEnumMember(node): void {
         // If there is no initializer, then this node is just the name of the member, so ignore.
+        if (node.initializer == null) {
+          return;
+        }
+        // any old literal
+        if (node.initializer.type === AST_NODE_TYPES.Literal) {
+          return;
+        }
+        // -1 and +1
         if (
-          node.initializer != null &&
-          node.initializer.type !== AST_NODE_TYPES.Literal
+          node.initializer.type === AST_NODE_TYPES.UnaryExpression &&
+          ['+', '-'].includes(node.initializer.operator) &&
+          node.initializer.argument.type === AST_NODE_TYPES.Literal
         ) {
-          context.report({
-            node: node.id,
-            messageId: 'notLiteral',
-          });
+          return;
         }
+
+        context.report({
+          node: node.id,
+          messageId: 'notLiteral',
+        });
       },
     };
   },
 
@@ -23,6 +23,16 @@ enum ValidNumber {
 }
     `,
     `
+enum ValidNumber {
+  A = -42,
+}
+    `,
+    `
+enum ValidNumber {
+  A = +42,
+}
+    `,
+    `
 enum ValidNull {
   A = null,
 }
@@ -121,6 +131,44 @@ enum InvalidExpression {
     },
     {
       code: `
+enum InvalidExpression {
+  A = delete 2,
+  B = -a,
+  C = void 2,
+  D = ~2,
+  E = !0,
+}
+      `,
+      errors: [
+        {
+          messageId: 'notLiteral',
+          line: 3,
+          column: 3,
+        },
+        {
+          messageId: 'notLiteral',
+          line: 4,
+          column: 3,
+        },
+        {
+          messageId: 'notLiteral',
+          line: 5,
+          column: 3,
+        },
+        {
+          messageId: 'notLiteral',
+          line: 6,
+          column: 3,
+        },
+        {
+          messageId: 'notLiteral',
+          line: 7,
+          column: 3,
+        },
+      ],
+    },
+    {
+      code: `
 const variable = 'Test';
 enum InvalidVariable {
   A = 'TestStr',