<p>In the field of research on the interaction between electrons and laser pulses, existing studies focus on the radiation characteristics under specific parameter conditions. However, research into the effects of a wider range of parameter changes is lacking. Within the classical electromagnetism framework, this paper employs numerical simulation methods to systematically investigate the influence of electron initial energy variations on the radiation characteristics produced during their cross-collisions with Gaussian laser pulses. Meanwhile the relationship between the peak radiated power of electron and the beam waist radius, the electron emission position and the initial energy of the electron is analyzed. The temporal distribution, spatial distribution and frequency spectrum of electron radiation is also compared and analyzed. The results show that under tight focusing conditions of the laser pulse, the radiation of moderate-energy electrons exhibit asymmetry, and the asymmetry of the radiation gradually weakens as the electron initial energy and the laser beam waist radius increase. For moderate-energy electrons, the rise in initial energy results in a rise in the peak radiated power of electron and a broadening of the spectral band pass. This study focuses on how the initial energy of electron affects nonlinear Thomson scattering, providing a new perspective for studying the cross-collision between electrons and the laser pulse.</p>