In this paper, a physical model and numerical method in cloud-in-cell (CIC) scheme for simulation of weak collisional effects are proposed. Collisions are introduced at reconstruction time in terms of a one-dimensional Fokker–Planck operator. The friction term of the collision operator is equivalent to the introduction of a velocity-dependent acceleration a (u)= –uγ (u) into the equation of motion of the, particles. The diffusion term is represented by finite differences over the nonuniform velocity grid. Collisional relaxation, of two Maxwellian beams. is studied. The numerical results are in good agreement with the analytical values.