We construct a family $I_{n_{\eps}}(f)_{t}$ of continuous stochastic processes that converges in the sense of finite dimensional distributions to a multiple Wiener-Itô integral $I_{n}^{H}(f1^{\otimes n}_{[0,t] })$ with respect to the fractional Brownian motion. We assume that $H>\frac{1}{2}$ and we prove our approximation result for the integrands $f$ in a rather general class.