Broadband terahertz (THz) waves were generated by optical parametric processes based on laser light scattering from the polariton mode of a nonlinear crystal. By using the parametric oscillation of a MgO-doped LiNbO3 crystal pumped by a nanosecond Q-switched Nd:YAG laser, we have realized a broadband, high-energy and compact THz-wave source. We report the development of a THz-wave parametric generator (TPG) using a small pump source with a short pulse width and a top-hat beam profile. These characteristics of the pump beam permit high-intensity pumping especially close to the output surface of the THz wave without thermal damage to the crystal surface. We also calculated the outcoupled THz wave for beams with two different intensity profiles: a top-hat beam (in this experiment) and a Gaussian beam (previously reported). The result shows the mechanism of the output energy and/or power enhancement.