In　this　paper　we　prove　that　for　certain　class　of　the　initial　data,　the　corresponding　solutions　of　the　3-D　viscous　primitive　equations　without　viscosity　blow　up　in　finite　time.　We　find　a　specific　solution　to　simplify　the　three　dimensional　systems,　and　furthermore,　we　construct　a　self-similar　solution　to　solve　the　blow-up　problem.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.