Flexible gridding has the potential of increasing the accuracy in numerical simulation of flow through hydrocarbon reservoirs within limitations in computing time and memory space. This paper is devoted to the description of a computational algorithm for two-phase immiscible, incompressible flows in an adaptive composite grid. An IMPES approach is applied. The pressure equation is discretized on locally refined grids with finite volume scheme. To solve this equation, a FAC method outlined by McCormick is used. For the transport equation, we propose the finite difference schemes : upwind are MUSCL. An object oriented programming language C++ is selected for the implementation. It provides a dynamic memory management and a convenient data structure for evolutive problems. Results for some examples illustrate the efficiency of proposed algorithm.