A conceptual design of a thermosyphonic Magnetohydrodynamic power generator is presented and its performance is numerically investigated. A simplified two-dimensional model of generator is considered. Liquid gallium is selected as working fluid. The left wall and right wall of thermosyphon are at constant temperature T-h and T-c, (T-h > T-C) respectively. Other walls and baffle are insulated. A constant magnetic field is applied horizontally. Separate pairs of electrodes are considered to conduct the generated current. A proper magnetic field reference is introduced to nondimensionalize the governing equations. A numerical code based on the finite volume technique is developed to solve the unsteady governing equations for a laminar natural convection flow. The effects of the Rayleigh number (Ra), Hartmann number (Ha), aspect ratio (Ar) and electric efficiency (K) on the thermo-fluid behaviour throughout the thermosyphon, on the induced electric current density, and on the generated power are investigated. Increasing the aspect ratio and Hartmann number, causes to decrease the natural convection effects, and reduces the Nusselt number. While increasing the Rayleigh number augments the effect of natural convection and consequently the generated power (W*), electric current density (J*), and electric field (E*) increases. It is seen that for a given Rayleigh number, there is a Hartmann number, an aspect ratio, and an electric efficiency, for which the generated power, W*, becomes maximum. For a given Rayleigh number and aspect ratio, it is shown that the generated power does not monotonically varies with Ha. It decreases by increasing Ha from certain values.