In the present paper we study the convergence of the solution of the two dimensional (2-D) stochastic Leray- model to the solution of the 2-D stochastic Navier-Stokes equations. We are mainly interested in the rate, as , of the following error function epsilon(alpha)(t) = sup(s is an element of[0,t])vertical bar u(alpha)(s) - u(s)vertical bar + integral(t)(0) vertical bar A(1/2)[u(alpha)(s) - u(s)]vertical bar(2) ds)(1/2), where u(alpha) and u are the solution of stochastic Leray-alpha model and the stochastic Navier-Stokes equations, respectively. We show that when properly localized the error function epsilon(alpha) converges in mean square as alpha -> 0 and the convergence is of order O(alpha). We also prove that epsilon(alpha) converges in probability to zero with order at most O(alpha).