In this paper, four key design parameters with a strong influence on the performance of a high-solidity variable pitch vertical axis wind turbine (VAWT) operating at low tip-speed-ratio (TSR) are addressed. To this aim, a numerical approach, based on a finite-volume discretization of two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) equations, on a multiple sliding mesh, is proposed and validated against experimental data. The self-pitch VAWT design is based on a straight-blade Darrieus wind turbine with blades that are allowed to pitch around a feathering axis, which is also parallel to the axis of rotation. The pitch angle amplitude and periodic variation are dynamically controlled by a four-bar linkage system. We only consider the efficiency at low and intermediate TSR; therefore, the pitch amplitude is chosen to be a sinusoidal function with a considerable amplitude. The results of this parametric analysis will contribute to define the guidelines for building a full-size prototype of a small-scale wind turbine of increased efficiency.