Index: lld/ELF/Config.h
===================================================================
--- lld/ELF/Config.h
+++ lld/ELF/Config.h
@@ -61,6 +61,9 @@
 // For tracking ARM Float Argument PCS
 enum class ARMVFPArgKind { Default, Base, VFP, ToolChain };
 
+// For --compress-debug-sections.
+enum class CompressDebugSectionsPolicy { None, Zlib, ZlibGnu };
+
 struct SymbolVersion {
   llvm::StringRef Name;
   bool IsExternCpp;
@@ -130,7 +133,7 @@
   bool BsymbolicFunctions;
   bool CallGraphProfileSort;
   bool CheckSections;
-  bool CompressDebugSections;
+  CompressDebugSectionsPolicy CompressDebugSections;
   bool Cref;
   bool DefineCommon;
   bool Demangle = true;
Index: lld/ELF/Driver.cpp
===================================================================
--- lld/ELF/Driver.cpp
+++ lld/ELF/Driver.cpp
@@ -700,15 +700,19 @@
   }
 }
 
-static bool getCompressDebugSections(opt::InputArgList &Args) {
+static CompressDebugSectionsPolicy getCompressDebugSections(opt::InputArgList &Args) {
   StringRef S = Args.getLastArgValue(OPT_compress_debug_sections, "none");
-  if (S == "none")
-    return false;
-  if (S != "zlib")
+  if (S == "zlib" || S == "zlib-gnu") {
+    if (!zlib::isAvailable())
+      error("--compress-debug-sections: zlib is not available");
+    if (S == "zlib")
+      return CompressDebugSectionsPolicy::Zlib;
+    if (S == "zlib-gnu")
+      return CompressDebugSectionsPolicy::ZlibGnu;
+  } else if (S != "none") {
     error("unknown --compress-debug-sections value: " + S);
-  if (!zlib::isAvailable())
-    error("--compress-debug-sections: zlib is not available");
-  return true;
+  }
+  return CompressDebugSectionsPolicy::None;
 }
 
 static std::pair<StringRef, StringRef> getOldNewOptions(opt::InputArgList &Args,
Index: lld/ELF/OutputSections.h
===================================================================
--- lld/ELF/OutputSections.h
+++ lld/ELF/OutputSections.h
@@ -108,6 +108,8 @@
   template <class ELFT> void writeTo(uint8_t *Buf);
   template <class ELFT> void maybeCompress();
 
+  StringRef finalName();
+
   void sort(llvm::function_ref<int(InputSectionBase *S)> Order);
   void sortInitFini();
   void sortCtorsDtors();
Index: lld/ELF/OutputSections.cpp
===================================================================
--- lld/ELF/OutputSections.cpp
+++ lld/ELF/OutputSections.cpp
@@ -183,8 +183,8 @@
   typedef typename ELFT::Chdr Elf_Chdr;
 
   // Compress only DWARF debug sections.
-  if (!Config->CompressDebugSections || (Flags & SHF_ALLOC) ||
-      !Name.startswith(".debug_"))
+  if (Config->CompressDebugSections == CompressDebugSectionsPolicy::None ||
+      (Flags & SHF_ALLOC) || !Name.startswith(".debug_"))
     return;
 
   // Create a section header.
@@ -205,6 +205,13 @@
   Flags |= SHF_COMPRESSED;
 }
 
+StringRef OutputSection::finalName() {
+  if (Config->CompressDebugSections == CompressDebugSectionsPolicy::ZlibGnu &&
+      !(Flags & SHF_ALLOC) && Name.startswith(".debug_"))
+    return Saver.save(".z" + Name.substr(1));
+  return Name;
+}
+
 static void writeInt(uint8_t *Buf, uint64_t Data, uint64_t Size) {
   if (Size == 1)
     *Buf = Data;
Index: lld/ELF/Writer.cpp
===================================================================
--- lld/ELF/Writer.cpp
+++ lld/ELF/Writer.cpp
@@ -1751,7 +1751,7 @@
   for (size_t I = 0, E = OutputSections.size(); I != E; ++I) {
     OutputSection *Sec = OutputSections[I];
     Sec->SectionIndex = I + 1;
-    Sec->ShName = In.ShStrTab->addString(Sec->Name);
+    Sec->ShName = In.ShStrTab->addString(Sec->finalName());
   }
 
   // Binary and relocatable output does not have PHDRS.
Index: lld/test/ELF/compress-debug-sections.s
===================================================================
--- lld/test/ELF/compress-debug-sections.s
+++ lld/test/ELF/compress-debug-sections.s
@@ -30,6 +30,21 @@
 # RUN:   FileCheck -check-prefix=ERR %s
 # ERR: unknown --compress-debug-sections value: zlib-gabi
 
+## Test GNU version.
+# RUN: ld.lld %t.o -o %t3 --compress-debug-sections=zlib-gnu
+
+# RUN: llvm-objdump -s %t3 | FileCheck %s --check-prefix=ZLIBGNUCONTENT
+# ZLIBGNUCONTENT:     Contents of section .zdebug_str:
+# ZLIBGNUCONTENT-NOT: AAAAAAAAA
+
+# RUN: llvm-readobj -s %t3 | FileCheck %s --check-prefix=ZLIBGNUFLAGS
+# ZLIBGNUFLAGS:       Section {
+# ZLIBGNUFLAGS:         Index:
+# ZLIBGNUFLAGS:         Name: .zdebug_str
+# ZLIBGNUFLAGS-NEXT:    Type: SHT_PROGBITS
+# ZLIBGNUFLAGS-NEXT:    Flags [
+# ZLIBGNUFLAGS-NEXT:      SHF_COMPRESSED
+
 .section .debug_str,"MS",@progbits,1
 .Linfo_string0:
   .asciz "AAAAAAAAAAAAAAAAAAAAAAAAAAA"