A commercial computational fluid dynamics (CFD) code is used to compute the flow field within the first-stage rotor and stator of a two-stage mixed flow pump. The code solves the 3D Reynolds-averaged Navier-Stokes equations in rotating and stationary cylindrical coordinate systems for the rotor and stator, respectively. Turbulence effects are modeled using a standard $k-ϵ$ turbulence model. Stage design parameters are rotational speed $890\hspace{0.17em}\text{rpm}$, flow coefficient $\varphi =0.116$, head coefficient $\psi =0.094$, and specific speed $2.01$ (5475 US). Results from the study include velocities, and static and total pressures for both the rotor and stator. Comparison is made to measured data for the rotor. The comparisons in the paper are for circumferentially averaged results and include axial and tangential velocities, static pressure, and total pressure profiles. Results of this study show that the computational results closely match the shapes and magnitudes of the measured profiles, indicating that CFD can be used to accurately predict performance.