Beam quality factor $M^{\text{2}}$ is the main parameter to characterize the transverse-mode property of high power laser. In view of the problem that beam quality analyzer can only be used to evaluate the beam quality of small caliber and low power laser, the principle and simulation of attenuation and compression technology of beam quality measurement of high power laser were studied. The simulation model of attenuation and compression module was established, and the thermal aberration of optical component under high power laser was studied by finite element method. The results show that the effect of the thermal aberration on the beam quality factor is less than 5% when the peak and valley (PV) value is less than 82 nm. If depolarization occurs when the beam passes through the attenuation component, the beam quality factor will be smaller. The influence of wavefront distortion caused by compression module on beam quality factor measurement was analyzed based on Zernick polynomial and beam quality factor calculation model. Through the Zemax simulation, the influence on beam quality factor measurement is less than 5% when the field of view between the incident light and the center optical axis of the attenuation and compression module is less than 7 °.