Many factors of intracavity perturbation can degrade output power and beam quality in high power passive Q-switching slab lasers. The experiment test on output beam quality of a passive Q-switching zig-zag slab laser has been performed by adopting Hartmann-Shack (H-S) wavefront sensor and Zernike modal reconstruction theory. In this way, peak value (PV) and root mean square (RMS) values of the wavefront aberration, and Zernike aberration of each order can be acquired accurately. Moreover, distribution of circle energy in far-field, point spread function (PSF) and other beam evaluation factors can also be obtained by further calculation, so the beam quality can be illuminated comprehensively. Results analysis show that the wavefront aberration of beam mainly concentrates in the frontal 10 ranks of Zernike aberration, mainly including the defocus A3, the low-order astigmatism A5, the coma aberration A6 and the spherical aberration A10 because of the crystal thermal effect and intracavity aberrated perturbation.