Based on the second-order moment method,considering astigmatic beam without rotational symmetry,the M4 parameters were adopted to describe the beam quality.The analytical expressions of beam-waist and divergence angle for astigmatic Gaussian beam without rotational symmetry were derived.And the astigmatic coefficient aZF was adopted to describe the astigmatic characteristics of laser beam.The M4- parameters (M4xx,M4yy,M4xy and Mr4) can be expressed by the astigmatic coefficient aZF.In addition,the astigmatic coefficient aZF and the principal M4 parameters can be calculated by measuring M4 parameters of the laser beam.When laser beam passes through aberration-free optical system,the propagation constants aZF,JZF1 and JZF2 remain unchanged.The obtained results have an important practical reference value for the design,manufacture and application of laser.