Marine currents may represent a renewable energy source characterized by a limited environmental impact. In Italy, the Strait of Messina seems to be suited for exploitation of this energy source. A vertical axis turbine, with blades oscillating about the pivotal axis according to the Voith–Schneider system, has been considered. This paper presents a preliminary theoretical investigation of the performance of this kind of turbine that may be employed to tap marine currents energy sources. The investigation is conducted by means of a simple momentum model based on the “single-disk single-streamtube” approach. The theoretical results are compared with experimental measurements. The adequate agreement between experimental and theoretical results shows that such a simple model may be able to predict the power coefficient and the operating range of the turbine.