This paper explores the efficient generation of Terahertz (THz) radiation using Sinh-Gaussian laser pulses in a uniform underdense homogenous collisional plasma. The study focuses on the nonlinear interaction between two Sinh-Gaussian pulses, which generates a nonlinear current density that results in the production of THz waves. The efficiency of THz generation is analyzed by examining the effects of the decentered parameter and collisional frequency. The results show that increasing the decentered parameter or decreasing the collisional frequency enhances the energy efficiency of the generated THz radiation. This research highlights the potential of this pulse shape for optimizing THz sources, advancing ultrafast optics, and terahertz technology. The study includes the derivation of basic formulas for the electric and magnetic fields of the laser beams, the motion of electrons, and the nonlinear ponderomotive force, leading to the governing equation for THz generation.This paper explores the efficient generation of Terahertz (THz) radiation using Sinh-Gaussian laser pulses in a uniform underdense homogenous collisional plasma. The study focuses on the nonlinear interaction between two Sinh-Gaussian pulses, which generates a nonlinear current density that results in the production of THz waves. The efficiency of THz generation is analyzed by examining the effects of the decentered parameter and collisional frequency. The results show that increasing the decentered parameter or decreasing the collisional frequency enhances the energy efficiency of the generated THz radiation. This research highlights the potential of this pulse shape for optimizing THz sources, advancing ultrafast optics, and terahertz technology. The study includes the derivation of basic formulas for the electric and magnetic fields of the laser beams, the motion of electrons, and the nonlinear ponderomotive force, leading to the governing equation for THz generation.