The purpose of this study is to explore Second harmonic generation (SHG) of high power Cosh-Gaussian beam in cold collisionless plasma. The ponderomotive force causes carrier redistribution from high field to low field region in presence of Cosh-gaussian beam thereby producing density gradients in transverse direction. The density gradients so produced results in electron plasma wave (EPW) generation at frequency of input beam. The EPW interacts with input beam resulting in production of 2nd harmonics. WKB and paraxial approximations are employed for obtaining 2nd order differential equation describing behavior of beam’s spot size against normalized distance. The impact of well established laser-plasma parameters on behavior of beam’s spot size and SHG yield are also analyzed. The focusing behavior of beam and SHG yield are enhanced with increase in density of plasma, radius of beam and decentred parameter and with decrease in intensity of beam. The results of current problem are really helpful for complete information of laser-plasma interaction physics.