A three-dimensional parallel Euler flow solver has been developed for the simulation of unsteady rotor-fuselage interaction aerodynamics on unstructured meshes. In order to handle the relative motion between the rotor and the fuselage, the flow field was divided into two zones, a moving zone rotating with the blades and a stationary zone containing the fuselage. A sliding mesh algorithm was developed for the convection of the flow variables across the cutting boundary between the two zones. A quasi-unsteady mesh adaptation technique was adopted to enhance the spatial accuracy of the solution and to better resolve the wake. A low Mach number pre-conditioning method was implemented to relieve the numerical difficulty associated with the low-speed forward flight. Validations were made by simulating the flows around the Georgia Tech configuration and the ROBIN fuselage. It was shown that the present method is efficient and robust for the prediction of complicated unsteady rotor-fuselage aerodynamic interaction phenomena.