In this paper, we construct a family of continuous stochastic processes that converges in law to the multiple Wiener-It$hat{o}$ integrals with respect to the subfractional Brownian motion with H > $frac{1}{2}$ for the integrand f in a rather general class of functions. Wemainly use Donsker and Stroock approximations and the techniques of the multiple Wiener-It$hat{o}$ integral with respect to the Wiener process.