Based in a very recent paper by Micchelli et al. [8], we present an algorithmic approach for computing the resolvent of composite operators: the composition of a monotone operator and a continuous linear mapping. The proposed algorithm can be used, for example, for solving problems arising in image processing and traffic equilibrium. Fur- thermore, our algorithm gives an alternative to Dykstra-like method for evaluating the resolvent of the sum of two maximal monotone operators.