This paper presents numerical computations of three bladed horizontal axis marine current turbines in a uniform free upstream current. The unsteady evolution of the turbine wake is taken into account by some three-dimensional software, developed to assess the disturbances generated in the sea. An unsteady Lagrangian method is considered for these computations using "Vortex Method"; a velocityvorticity numerical implementation of the Navier-Stokes equations. The vortex flow is discretised with particles carrying vorticity, which are advected in a Lagrangian frame. The present paper aims at presenting results on both power and thrust coefficient (C P and C T) predictions and wake characterisation, up to ten diameters downstream of the turbine. Moreover, two different marine current turbines configurations are considered: one is taken from literature [1] and the second one is an open-modified version of turbine inspired from previous works [2]. Highlights ► We developed a numerical software for the computation of marine current turbine. ► We used an unsteady Lagrangian implementation of the Navier-Stokes equations. ► Two different turbines are considered, one of them is taken from the literature [1]. ► Both power/thrust coefficients and wake are computed with the same numerical tool. ► All the numerical results are compared to experiments