We present an efficient numerical algorithm to approximate the statistical moments of stochastic problems, in the presence of models with different fidelities. The method extends the multi-fidelity approximation method developed in [18,26]. By combining the efficiency of low-fidelity models and the accuracy of high-fidelity models, our method exhibits fast convergence with a limited number of high-fidelity simulations. We establish an error bound of the method and present several numerical examples to demonstrate the efficiency and applicability of the multi-fidelity algorithm.