In this paper, we study the complexity of information of approximation problem on the multivariate Sobolev space with bounded mixed derivative MW r p,α (T d ), 1 < p < ∞, in the norm of Lq(T d ), 1 < q < ∞, by adaptive Monte Carlo methods. Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of this problem. Keywords: adaptive Monte Carlo method, Sobolev space with bounded mixed derivative, asymptotic order MSC(2000): 41A46, 41A63, 65C05, 65D99