In this paper an effective method is developed to study aerodynamic characteristics of a flying wing micro air vehicle (MAV). The method is based on momentum source method (MSM), low Mach number preconditioning and lower-upper symmetric Gauss-Seidel (LU-SGS) implicit dual time-stepping algorithm on hybrid dynamic meshes. The S-A turbulence model is also applied to capture flow separation. Momentum source items are utilized to replace the propeller in the numerical simulation by simplifying the unsteady flow into a steady one. Compared with wind tunnel experimental results, the computed results indicate that the method developed is capable of dealing with steady and unsteady aerodynamic characteristics of flying wing MAV