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A repulsive vortex-vortex interaction model was used to numerically study the melting transition of the two-dimensional vortex system with Monte Carlo method. Then a δ-function-like peak in the specific heat was observed and the internal energy showed a sharp drop at the melting temperature, which indicated that there exists a first-order melting transition at finite temperatures. The Lindemann criterion was also investigated and valid, but different from previous simulation results.