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AC loses in high superconductor (HTS) thin film are evaluated by element-free Galerkin method with double exponential formula. The shielding current density in an HTS is necessary information to calculate the AC loss. Formulation of the electromagnetic behavior of the shielding current density gives a system. However, improper integrals appear as coefficients of the system and the integrand have a stronger singularity with decreasing thickness of the HTS. The code for the shielding current analysis in HTS by element-free Galerkin method is developed. In order to evaluate the improper integrals accurately, the double exponential formula is adopted in the code. Results of the computation shows that the spatial distribution of the shielding current density is calculated with a high accuracy.