In PIC (particle‐in‐cell) simulations, the Takizuka–Abe (TA) model is widely used as a basic Coulomb collision model. For the weighted particle simulations, some collision models, such as the “rejection model” and the “merging model,” have been developed by expanding the TA model. These models do not conserve the total momentum or total energy, but can nearly conserve them, on average. We here develop a new model by expanding the TA model, which conserves both the total energy and total momentum in each time step. In the test simulations, the new model accomplishes the exact conservation of both energy and momentum. We examine the temperature relaxation and the velocity distribution function (VDF) for the model validation. In the merging model, temperature relaxation is inappropriate and the VDFs deviate from Maxwell distribution. In the new model, the temperature relaxation is correctly achieved and the VDFs are maintained Maxwellian.