M2 factor measuring system which based on crossed defocus gratings is theatrical analyzed. This instrument can get nine intensity distributions of different positions near the beam waist. The M2 factor is determined by calculating the beam waist using the second moment method and curve-fitting. According to the theory of Gaussian beam propagation and transformation; using the zeroth-order and multi-modes Gaussian beam, measured errors as functions of beam waist, positions and modes distribution are analyzed. If zeroth-order Gaussian beam waist radius or the zeroth-order Gaussian beam waist radius corresponding to multi-modes beam was properly controlled, the measuring system can work well in a large range. The guidance for the M2 factor measuring system is provided by this analysis.