Due　to　the　small　parameter,　high　order　derivatives　and　nonlinear　term,　it　takes　a　long　time　to　reach　the　steady　state　in　the　simulation　of　the　molecular　beam　epitaxy　(MBE)　model.　In　this　work,　based　on　the　numerical　scheme　in　Qiao　et　al.　(2011)　and　the　good　properties　it　holds,　we　introduce　two　types　of　adaptive　time-stepping　methods,　in　which　the　physical　quantities　like　energy　or　roughness　are　involved　to　produce　time　steps.　Similarly　to　the　spatial　adaptive　method,　we　take　equidistribution　of　the　physical　quantities　in　time　direction　to　control　the　simulation　error.　The　numerical　experiment　shows　that　the　computational　time　is　significantly　saved　by　these　methods.　(C)　2019　Elsevier　Ltd.　All　rights　reserved.