Three-dimensional numerical computations for a single bubble rising in a liquid metal within a rectangular enclosure in a uniform vertical magnetic field are carried out. In this study, the bubble shape, the velocity field and the electric current density field interact with one another under the influence of the vertical magnetic field. This is a triple simultaneous problem. The pressure and the electric potential fields are obtained with an iterative procedure by the HSMAC method. The numerical results exhibit that the rising velocity of the bubble for the range of Hartmann number 0<Ha<75 is slightly larger than that of Ha=0 because of the drag reduction due to suppression effect on flow separation behind the bubble. On the other hand, the bubble rising velocity decreases monotonously with the increase in the Hartmann number for Ha>75 owing to deceleration effect on the fluid flow by the magnetic field. The bubble elongates in the direction of the uniform magnetic field because of the modification of the pressure distribution by the Lorentz force.