A bi-axial cross-flow water turbine is numerically simulated to evaluate its performance with a view to carrying out experiments on a prototype. Two axes of rotation and a chain-pulley system allow for an innovative blade kinematics. Indeed, the angle of attack of the blades is constant over a portion of their trajectory. This is a sought-after characteristics but difficult to obtain for conventional cross-flow turbines. 2D URANS k-ω SST simulations are carried out. Experimental data from an oscillating airfoil case are used to validate the numerical simulation process. The impact of solidity for one-blade turbine and the impact of the number of blades at isosolidity are studied. The unbalance performance between the upstream and downstream parts of the turbine are also investigated.