A semi-implicit method for solving the full compressible resistive magnetohydrodynamic equations in three dimensions is presented. The method is designed for use in the modeling of fusion plasmas in magnetic confinement devices. The method is unconditionally stable with respect to the fast compressional modes. The time step is limited instead by the slower shear Alfvén motion. The computing time required for one time step is essentially the same as that for explicit methods. The code is applied to resistive instabilities in cylindrical tokamak equilibria.