Large eddy simulation of the complete stage of a mixed-flow pump is presented. The computation takes full account of the interaction between the rotating impeller and the stationary casing by using a multi-frame-of-reference dynamic overset grid approach. A streamline-upwind finite element formulation with second-order accuracy both in time and space is used for discretizing the governing equations. It is implemented in parallel by a domain decomposition programming model, and therefore, it can be applied to a large scale computation on a distributed-memory parallel computer. Internal flow of a high-specific-speed mixed-flow pump stage (ωs=2.1) is simulated to test the validity of the proposed method under four operating conditions: the design point (Q/Qd=100%) and three off-design points (Q/Qd=60%, 80% and 120%). For all the cases computed herein, the predicted total pump head and the unsteady fluid forces on the impeller agreed well with the measured values.