A three-dimensional parallel Euler flow solver has been developed for the simulation of unsteady rotor aerodynamics on unstructured meshes. The time integration was achieved by using a second-order accurate point Gauss-Seidel relaxation method. A cell-centered finite-volume flux discretization was used in conjunction with the Roe's flux-difference splitting. To simulate the unsteady rotor wake effectively, the flow field was divided into two zones. The upper zone contains the rotor blades and rotates with them, and the lower zone is stationary and covers the far wake. A sliding mesh algorithm was developed for the convection of How variables across the cutting boundary between the two zones. Quasi-unsteady mesh adaptation was adopted to enhance the spatial accuracy of the solution. Mesh deformation resulting from the blade motion in forward flight was handled by using a spring analogy and cell-edge collapsing. Validation was made for flow around the rotor blades in hover and in forward flight. It was shown that the present method is grid-efficient and robust for the prediction of complex unsteady rotor flow fields.