When one fluid displaces others, the predominating physical process occurs along the moving interface between the fluids. This paper is devoted to the description of a computational algorithm for two-phase immiscible, incompressible flows in an adaptive composite grid to track the moving front. This algorithm is based on an IMPES method applied to a convergent and conservative finite volume scheme for the pressure equation, together with the finite difference scheme, upwind and MUSCL, for the transport equation on grids with local refinement.