The linear system which appears in the shielding current analysis of the HTS film without a crack has the symmetric and dense coefficient matrix. In this study, the H-matrix-based preconditioning has been proposed for accelerating the conjugate gradient (CG) method which is adopted as a solver of the linear system and its performance has been investigated. The result of computations shows that the H-matrix-based preconditioned CG method is much faster than the standard one.