This research presents a study to explain the nonlinear self-focusing of Gaussian laser beam with right circular polarization (RCP) in the presence of longitudinal magnetic field, then propagation in plasma. Due to self-focusing of (RCP) laser beam inside plasma, the intensity inside the system will reach 10 18 W.cm -2 or more which is enough to excite a terahertz radiation by relativistic nonlinearity. The terahertz radiation generation is depending on the down conversion of three wave mixing technique and on the fulfilling the phase matching conditions between pump waves (laser beam), plasma wave and generated terahertz wave. By designing appropriate Matlab programs, the final equations of self-focusing effect and terahertz generation have been solved numerically. The calculations show that the increasing of both the initial intensity and the initial radius of the laser beam are leading to increase the nonlinear self-focusing and thus the terahertz radiation generation. One of the