The moving particle semi-implicit (MPS) method is a fully lagrangian particle method for incompressible flow, which is based on particles and their interactions. In this method, grids are unnecessary and a semi-implicit algorithm is used. Using MPS method, the Rayleigh-Taylor instability (RTI) between Silicon oil and water triggered by the buoyancy force is simulated. The results are in consistent with the linear analysis of RTI. The shape of bubbles and spikes obtained in the calculation agrees well with the experimental observations.