The near flat-top Gaussian beam, which finds significant applications in energy amplification, laser processing, nonlinear frequency transformation, and atmospheric turbulence studies, has received limited attention regarding its transverse mode field distribution characteristics during spatial transmission and amplification. In this study, we simulated the spatial transmission and amplification processes of the near flat-top Gaussian beam using the Collins diffraction equation and a traditional side-pumping gain model. To validate our simulations, we conducted experiments employing a gradual soft-edged aperture to produce a near flat-top Gaussian beam. Our findings revealed that during free transmission, the near flat-top Gaussian beam evolved into a Gaussian-like beam, and a secondary peak emerged when amplified by a conventional laser diode side-pumping amplifier. These results underscored the necessity of using an image transfer system to maintain the energy uniformity of the near flat-top Gaussian beam during amplification. Furthermore, we identified the optimal shaping parameter of the Gaussian beam with a soft-edged aperture to be approximately 2.3. By utilizing an image transfer system and a two-stage amplifier, we successfully amplified the beam energy post-shaping. Ultimately, we achieved a near flat-top Gaussian beam with an energy of 219.5 mJ and an energy root-mean-square (RMS) normalized deviation of 0.144, compared to the initial Gaussian beam, which had an energy of 52.3 mJ and an energy RMS normalized deviation of 1.434.