In order to study the hydrodynamic performance of multiple vertical tidal current turbines, an analysis model based on free vortex model is proposed. By comparing with experiment data, the present model can obtain reasonable results. Then the hydrodynamic performance of twin-turbine and quad-turbine systems are studied using the present model. For twin-turbine system, five sets of turbines spacing and three sets of rotation direction are researched. And five sets of rotation direction are researched for quad-turbine system with one turbine spacing. By comparison, it is shown that positive effect on the relative power coefficient can be found at high TSR when turbines are side-by-side arrangement. At the same time, in most cases, it can obtain a higher relative power coefficient when turbines are rotating inward and have a smaller spacing. Due to the low computational time, the present method can be used in preliminary study on array arrangement of vertical axis tidal current turbine.