This paper presents simulation and control design for a subsea pump system driven by a permanent magnet synchronous linear motor. Linear and non-linear models are established to simulate the electrical, mechanical and fluid characteristics of the overall system. Based on simulation results, a linear but time-variant simplified model with parameter uncertainty is set up to enable design of controllers for the system. The parameter uncertainty is bounded by two extreme load conditions. Three control approaches are studied and compared on the basis of robustness and performance. Full simulations and tests are carried out to prove the design.