Abstract: In particle-in-cell simulation of plasma, TA and Nanbu models have been widely used for Coulomb collision. Both models require all particles to collide. In this paper, a cross-section-based method is introduced to give a probability of Coulomb collision for each particle pair and accelerate the computation. To test this method, the relaxations of an electron gas due to e-e collisions were simulated. Comparing the simulated with the theoretical values of velocity distribution function, electron temperature, the ratio of electron temperature in x, y direction to electron temperature, the accuracy of the cross-section-based method was verified. The calculation efficiency of this method can be improved by more than 40% than the TA model at the same small time step. Furthermore, at a large time step, the simulations show agreement with the theoretical solutions, the efficiency is also improved than the Nanbu model. The simulation about the equilibration of electron and ion temperature showes that this method is also suitable for e-i collisions. Therefore in the acceleration of simulating Coulomb collision, this method has two advantages as follows: first, there is a small number of particles to collide within a step, and second, it is suitable for large time steps.