Summary: We propose a fast and robust finite difference method for Merton’s jump diffusion model (cf. [R. C. Merton, J. Financ. Econ. 3, No. 1–2, 125–144 (1976; Zbl 1131.91344)]), which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase the efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreement with the exact solutions of the jump-diffusion model.