diff --git a/llvm/lib/MC/MCParser/MasmParser.cpp b/llvm/lib/MC/MCParser/MasmParser.cpp
--- a/llvm/lib/MC/MCParser/MasmParser.cpp
+++ b/llvm/lib/MC/MCParser/MasmParser.cpp
@@ -1099,6 +1099,14 @@
     tok = &Lexer.Lex();
   }
 
+  // Recognize and bypass line continuations.
+  while (tok->is(AsmToken::BackSlash) &&
+         Lexer.peekTok().is(AsmToken::EndOfStatement)) {
+    // Eat both the backslash and the end of statement.
+    Lexer.Lex();
+    tok = &Lexer.Lex();
+  }
+
   if (tok->is(AsmToken::Eof)) {
     // If this is the end of an included file, pop the parent file off the
     // include stack.
diff --git a/llvm/test/tools/llvm-ml/line_continuations.test b/llvm/test/tools/llvm-ml/line_continuations.test
new file mode 100644
--- /dev/null
+++ b/llvm/test/tools/llvm-ml/line_continuations.test
@@ -0,0 +1,17 @@
+# RUN: llvm-ml -filetype=asm %s | FileCheck %s
+
+.code
+
+t1:
+mov eax, \
+    ebx
+# CHECK: t1:
+# CHECK-NEXT: mov eax, ebx
+
+t2:
+mov eax, [ebx + \
+          1]
+# CHECK: t2:
+# CHECK-NEXT: mov eax, dword ptr [ebx + 1]
+
+END