The　extinction　and　the　stationary　distribution　to　a　stochastic　SEIR　epidemic　model　with　nonlinear　incidence　rate　in　a　population　of　varying　size　are　discussed.　Under　moderate　conditions,　the　existence-and-uniqueness　of　the　global　solution,　exponential　stability　and　the　stationary　distribution　with　ergodicity　are　obtained.　By　means　of　linearization　and　Fourier　transform,　we　prove　that　the　solution　obeys　a　fourdimensional　normal　distribution,　and　the　mean　and　the　variance　matrix　are　followed.　Then　numerical　simulations　are　carried　out　to　illustrate　our　results.　©　2018,　Chinese　Academy　of　Sciences.　All　right　reserved.