To　avoid　finding　the　stationary　distributions　of　stochastic　differential　equations　by　solving　the　nontrivial　Kolmogorov-Fokker-Planck　equations,　the　numerical　stationary　distributions　are　used　as　the　approximations　instead.　This　paper　is　devoted　to　approximate　the　stationary　distribution　of　the　underlying　equation　by　the　Backward　Euler-Maruyama　method.　Currently　existing　results　(Mao　et　al.,　2005;　Yuan　et　al.,　2005;　Yuan　et　al.,　2004)　are　extended　in　this　paper　to　cover　larger　range　of　nonlinear　SDEs　when　the　linear　growth　condition　on　the　drift　coefficient　is　violated.　©　2014　Elsevier　B.V.　All　rights　reserved.