The propagation of the atom laser beam with non-conservation quality factor is discussed based on the theory of ABCD formulation of propagation of a time-dependent quantum system. The equation for the quasi-continuous atom laser beam wave-function is given by Schrodinger equation, the beam width, divergence curvature radius and quality factor were introduced to represent the atom laser beam whose transverse potential could be separated. For the conservative quality factor system in some direction, the propagator of ABCD formulation can be got. The propagation of the atom laser beam is discussed during the interacting with Bose-Einstein condensation (BEC), the propagation with the trap on and the free propagation with the trap off whose potential can be separated by x and y. Authors′ methods and results are compared with Yann′s.