As the core component of laser technology, the performance of lasers directly affects the effectiveness of applications. The beam quality is one of the important indicators for evaluating the performance of lasers. Studying the factors and their mechanisms that affect the beam quality of lasers is of great significance for improving the performance and application effects of lasers. Designing a mathematical model for the influence of relevant factors on the beam quality of lasers is crucial. Using M2 factor as the evaluation criterion for laser beam quality, ignoring the influence of coherent components, a Zernike spherical aberration coefficient impact model on laser beam quality is constructed. Construct a model of the impact of air thermal effect on laser beam quality based on the same correlation between the root mean square of phase distortion and the root mean square of light intensity distribution. Clarify the expression of the light field distribution of Gaussian beams at the orbit, construct a model of the effect of self focusing on the quality of laser beams based on the "Talanov" principle, and comprehensively construct a comprehensive mathematical model of the influence of relevant factors on the quality of laser beams by integrating three types of influence models. After adjusting each relevant factor one by one, the numerical simulation results of the model are completely consistent with the actual situation, proving the practicality of the model.