A numerical method is developed to predict the aerodynamic characteristics of rigid coaxial rotor. The method uses the compressible Navier-Stokes (N-S) equation described by arbitrary Lagrange Euler (ALE) to solve the flow field. A low numerical dissipative Roe format for spatial dispersion is adopted. Multiple overset grid method is used to simulate the motion of the coaxial rotor. A delta trim method is implemented to simplify the calculation of Jacobin matrix for rigid coaxial rotor trim. First, the aerodynamic performance of the Harrington-2 coaxial rotor in hover is calculated. Then, the hover and forward flight states of a 2 m diameter coaxial rotor are calculated and compared with the experimental values. The results show that, the error of the calculation result and the test value is less than 3% under the typical state, and the error of the torque coefficient is less than 5%. The numerical method has a high capture precision for the vortex wake characteristics of the rigid coaxial rotor, and can effectively simulate the detailed characteristics of the complex flow fluid in hover and the low-speed forward flight states.