We have developed a lattice-Boltzmann model from previous models for multiphase fluid flows to simulate Rayleigh-Taylor instability.A force has been introduced and a 9-velocity square lattice is used.The conservation equation of total mass and momentum can be derived using Chapman-Enskog multiscale expansions.Using this model we have obtained the linear growth and nonlinear growth of bubbles and the mushrooms produced by Rayleigh-Taylor instability.