A numerical method is developed to solve the solutions of the Euler/Navier-Stokes equations for investigating the flowfileds of the flapping wings. It uses a third-order modified Osher-Chakravarthy (MOC) upwind finite-volume scheme for the convective terms and a second-order central finite-volume scheme for the viscous terms. A Diagonal Dominant Alternating Direction Implicit scheme (DDADI) coupling with an implicit residual smoothing is used for the time integration to achieving fast convergence of the proposed numerical method. The Baldwin-Lomax algebraic turbulent model is applied for calculating the turbulence flows at high Reynolds numbers. Quantitative and understanding simulations as a function of the plunging frequency, mean angle of attack, plunging amplitude and pitching angle are calculated. It is found that the mean thrust output and propulsion efficiency are independent of the mean angle of attack but dependent of the reduce frequency. The mean lift is linear shift while increasing the mean angle of attack.