Punishment　has　been　proved　to　be　an　effective　mechanism　to　sustain　cooperation　among　selfish　individuals.　In　previous　studies,　punishment　is　unidirectional:　an　individual　i　can　punish　j　but　j　cannot　punish　i.　In　this　paper,　we　propose　a　mechanism　of　mutual　punishment,　in　which　the　two　individuals　will　punish　each　other　if　their　strategies　are　different.　Because　of　the　symmetry　in　imposing　the　punishment,　one　might　expect　intuitively　the　strategy　to　have　little　effect　on　cooperation.　Surprisingly,　we　find　that　the　mutual　punishment　can　promote　cooperation　in　the　spatial　public　goods　game.　Other　pertinent　quantities　such　as　the　time　evolution　of　cooperator　density　and　the　spatial　distribution　of　cooperators　and　defectors　are　also　investigated.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.