The main objective of this paper is to carry out a rigorous hydrodynamic analysis of gulf-stream turbines and determine power for a range of flow and geometric parameters. For the purpose, a computational tool based on the vortex lattice method (VLM) is developed. Velocity of the flow on the turbine blades, in relation to the free-stream velocity, is determined through induction factors. The geometry of trailing vortices is taken to be helicoidal. The VLM code is validated by comparing its results with other theoretical and experimental data corresponding to flows about finite - aspect ratio foils, swept wings and a marine current turbine. The validated code is then used to study the performance of the prototype gulfstream turbine for a range of parameters. Power and thrust coefficients are calculated for a range of tip speed ratios and pitch angles. Of all the cases studied, the one corresponding to tip speed ratio of 8 and uniform pitch angle 2° produced the maximum power of 41.3 [kW] in a current of 1.73 [m/s]. The corresponding power coefficient is 0.45 which is slightly less than the Betz limit power coefficient of 0.5926. The VLM computational tool developed for the research is found to be quite efficient in that it takes only a fraction of a minute on a regular laptop PC to complete a run. The tool can therefore be efficiently used or integrated into software for design optimization.