This paper presents a 3-D compositional numerical simulator of alkali/surfactant/polymer (ASP) flooding. It takes into consideration 5 major mass-transfer processes (convection, diffusion-dispersion, liquid-liquid transfer, liquid-solid transfer and chemical reactions) and all important phenomena such as decrease of interfacial tension with synergism, variation of each phase residual saturation and relative permeability, polymer solution behavior (viscosity, rheology, residual resistance factor, in-situ gelation, etc.) and mobility control, fast and long-term alkali losses by different factors (ion exchanges, acid oil, CO2, polymer and rock), chemical adsorptions in presence of alkali, fluid and rock compressibihties, capillary pressure, gravity, etc. All phenomenological parameters in this simulator have definite physical senses and are obtainable from experimental data without extra assumption so that it is more capable to simulate real problems. This simulator can be applied to simulate different chemical flooding processes using polymer, alkali and/or surfactant agents with any combination. It has been verified by comparing the results of calculation with experimental data and it is a reliable tool for simulating and forecasting ASP flooding processes. A complete series of runs presented in this paper make understanding various mechanisms and parameter effects such as ASP synergistic actions, dynamic and equilibrium interfacial tensions, fluid viscosities, alkali consumption and other chemical losses, injection strategy, etc. The studies are very useful to guide ASP field application. The forecasting results of a real AP flooding pilot by using this simulator are presented in the paper.