In this work, in-house computational fluid dynamics (CFD) code was utilized to simulate a cross-flow vertical-axis marine current turbine (straight-bladed Darrieus type). Particular emphasis was placed on the influence of interaction between vortices and blades on hydrodynamic performance. A physical transient-rotor–stator model with a sliding mesh technique was used to capture changes in flow field at a particular time step. The Spalart–Allmaras turbulence model was adopted for the turbulence. For a Darrieus-type marine current turbine, hydrodynamic characteristics such as power coefficient and flow behavior were then numerically investigated. The results suggest that vortices shed from previous blade passages and the close encounter of a rotor blade with these vortices can cause a variation in performance for this type of turbine during operation at different tip speed ratios.