diff --git a/lib/MC/MCParser/ELFAsmParser.cpp b/lib/MC/MCParser/ELFAsmParser.cpp
index ddf988faa64..072befadd5f 100644
--- a/lib/MC/MCParser/ELFAsmParser.cpp
+++ b/lib/MC/MCParser/ELFAsmParser.cpp
@@ -118,6 +118,9 @@ public:
   bool ParseDirectiveSection(StringRef, SMLoc);
   bool ParseDirectiveSize(StringRef, SMLoc);
   bool ParseDirectivePrevious(StringRef, SMLoc);
+
+private:
+  bool ParseSectionName(StringRef &SectionName);
 };
 
 }
@@ -155,11 +158,43 @@ bool ELFAsmParser::ParseDirectiveSize(StringRef, SMLoc) {
   return false;
 }
 
+bool ELFAsmParser::ParseSectionName(StringRef &SectionName) {
+  // A section name can contain -, so we cannot just use
+  // ParseIdentifier.
+  SMLoc FirstLoc = getLexer().getLoc();
+  unsigned Size = 0;
+
+  for (;;) {
+    StringRef Tmp;
+    unsigned CurSize;
+
+    SMLoc PrevLoc = getLexer().getLoc();
+    if (getLexer().is(AsmToken::Minus)) {
+      CurSize = 1;
+      Lex(); // Consume the "-".
+    } else if (!getParser().ParseIdentifier(Tmp))
+      CurSize = Tmp.size();
+    else
+      break;
+
+    Size += CurSize;
+    SectionName = StringRef(FirstLoc.getPointer(), Size);
+
+    // Make sure the following token is adjacent.
+    if (PrevLoc.getPointer() + CurSize != getTok().getLoc().getPointer())
+      break;
+  }
+  if (Size == 0)
+    return true;
+
+  return false;
+}
+
 // FIXME: This is a work in progress.
 bool ELFAsmParser::ParseDirectiveSection(StringRef, SMLoc) {
   StringRef SectionName;
-  // FIXME: This doesn't parse section names like ".note.GNU-stack" correctly.
-  if (getParser().ParseIdentifier(SectionName))
+
+  if (ParseSectionName(SectionName))
     return TokError("expected identifier in directive");
 
   std::string FlagsStr;
diff --git a/test/MC/ELF/section.s b/test/MC/ELF/section.s
new file mode 100644
index 00000000000..4622cb41592
--- /dev/null
+++ b/test/MC/ELF/section.s
@@ -0,0 +1,11 @@
+// RUN: llvm-mc -filetype=obj -triple x86_64-pc-linux-gnu %s -o - | elf-dump  | FileCheck %s
+
+// Test that these names are accepted.
+
+.section	.note.GNU-stack,"",@progbits
+.section	.note.GNU-,"",@progbits
+.section	-.note.GNU,"",@progbits
+
+// CHECK: ('sh_name', 18) # '.note.GNU-stack'
+// CHECK: ('sh_name', 34) # '.note.GNU-'
+// CHECK: ('sh_name', 45) # '-.note.GNU'