仔细查看实际可用的内容：

edd@max:~$apt-cache search mingw-

libassuan-mingw-w64-dev - IPC library for the GnuPG components -- Windows port

libgcrypt-mingw-w64-dev - LGPL Crypto library - Windows development

libgpg-error-mingw-w64-dev - library of error values and messages in GnuPG (Windows development)

libksba-mingw-w64-dev - X.509 and CMS support library (Windows development)

libnpth-mingw-w64-dev - replacement for GNU Pth using system threads (Windows dev)

binutils-mingw-w64 - Cross-binutils for Win32 and Win64 using MinGW-w64

binutils-mingw-w64-i686 - Cross-binutils for Win32 (x86) using MinGW-w64

binutils-mingw-w64-x86-64 - Cross-binutils for Win64 (x64) using MinGW-w64

g++-mingw-w64 - GNU C++ compiler for MinGW-w64

g++-mingw-w64-i686 - GNU C++ compiler for MinGW-w64 targeting Win32

g++-mingw-w64-x86-64 - GNU C++ compiler for MinGW-w64 targeting Win64

gcc-mingw-w64 - GNU C compiler for MinGW-w64

gcc-mingw-w64-base - GNU Compiler Collection for MinGW-w64 (base package)

gcc-mingw-w64-i686 - GNU C compiler for MinGW-w64 targeting Win32

gcc-mingw-w64-x86-64 - GNU C compiler for MinGW-w64 targeting Win64

gdb-mingw-w64 - Cross-debugger for Win32 and Win64 using MinGW-w64

gdb-mingw-w64-target - Cross-debugger server for Win32 and Win64 using MinGW-w64

gfortran-mingw-w64 - GNU Fortran compiler for MinGW-w64

gfortran-mingw-w64-i686 - GNU Fortran compiler for MinGW-w64 targeting Win32

gfortran-mingw-w64-x86-64 - GNU Fortran compiler for MinGW-w64 targeting Win64

gnat-mingw-w64 - GNU Ada compiler for MinGW-w64

gnat-mingw-w64-base - GNU Ada compiler for MinGW-w64 (base package)

gnat-mingw-w64-i686 - GNU Ada compiler for MinGW-w64 targeting Win32

gnat-mingw-w64-x86-64 - GNU Ada compiler for MinGW-w64 targeting Win64

gobjc++-mingw-w64 - GNU Objective-C++ compiler for MinGW-w64

gobjc++-mingw-w64-i686 - GNU Objective-C++ compiler for MinGW-w64 targeting Win32

gobjc++-mingw-w64-x86-64 - GNU Objective-C++ compiler for MinGW-w64 targeting Win64

gobjc-mingw-w64 - GNU Objective-C compiler for MinGW-w64

gobjc-mingw-w64-i686 - GNU Objective-C compiler for MinGW-w64 targeting Win32

gobjc-mingw-w64-x86-64 - GNU Objective-C compiler for MinGW-w64 targeting Win64

libz-mingw-w64 - compression library - Windows runtime

libz-mingw-w64-dev - compression library - Windows development files

mingw-ocaml - ocaml-mingw-w64 transitional dummy package

mingw-w64 - Development environment targeting 32- and 64-bit Windows

mingw-w64-common - Common files for Mingw-w64

mingw-w64-i686-dev - Development files for MinGW-w64 targeting Win32

mingw-w64-tools - Development tools for 32- and 64-bit Windows

mingw-w64-x86-64-dev - Development files for MinGW-w64 targeting Win64

ocaml-mingw-w64 - OCaml cross-compiler based on mingw -- Meta-package

ocaml-mingw-w64-i686 - OCaml cross-compiler based on mingw -- 32 bit compiler

ocaml-mingw-w64-x86-64 - OCaml cross-compiler based on mingw -- 64 bit compiler

edd@max:~$

所以sudo apt-get install gcc-mingw-w64可能是你想要的,而且你应该通过设置适当的编译器选项(可能是-m32)来获得32位可执行文件.