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.　(C)　2014　Elsevier　B.V.　All　rights　reserved.