Self-focusing a laser beam in collisional plasma is investigated under the weak relativistic-ponderomotive nonlinearity. In this case, the plasma equilibrium density is modified and it causes generation of the nonlinearity due to the Ohmic heating of electrons, collisions, and the weak relativistic-ponderomotive force during the interaction of the laser beam with the plasma. Our theoretical and simulation results show that a significant nonlinearity in laser self-focusing can occur under the weak relativistic-ponderomotive regime for some appropriate simulation parameters.