An implicit higher-order discontinuous Galerkin(DG) spatial discretization for the compressible Euler equations in a rotating frame of reference is presented and applied to a rotor in hover using hexahedral grids. Instead of auxiliary methods like grid adaptation,higher-order simulations (fourth- and fifth- order accuracy) are adopted. Rigorous numerical experiments are carefully designed,conducted and analyzed. The results show generally excellent consistence with references and vigorously demonstrate the higher-order DG method’s better performance in loading distribution computations and tip vortex capturing, with much fewer degrees of freedom (DoF). Detailed investigations on the outer boundary conditions for hovering rotors are presented as well. A simple but effective speed smooth procedure is developed specially for the DG method. Further results reveal that the rarely used pressure restriction for outlet speed has a considerable advantage over the extensively adopted vertical speed restriction.