Numerical techniques are proposed for accelerating a linear-system solver appearing in the virtual-voltage method. After the proposed techniques are implemented to a numerical code for analyzing the shielding current density in a high-temperature superconducting film, their performance is numerically evaluated. The results of computations show that, if GMRES is incorporated as a linear-system solver, the speed of the virtual-voltage method will be remarkably enhanced. Moreover, it is also found that the implementation of the H-matrix method to matrix-vector multiplications in GMRES will further improve the speed of the virtual voltage method.