This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear Schr(o)dinger equation with a Stark potential.By using the variational characterization of corresponding ground state,the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ ={u ∈ H1; ∫RN [x|2|u|2dx ＜ +o}.Moreover,an interesting concentration property of the blow-up solutions with critical mass is gotten,which reads that |u(t,x)|2→‖Q‖2L2δx =x1 as t→ T.