Drug resistance of mutations V32I, G48V, I50V, I54V, and I84V in HIV-1 protease (PR) was found in clinical treatment of HIV patients with the drug amprenavir (APV). In order to elucidate the molecular mechanism of drug resistance associated with these mutations, the thermodynamic integration (TI) and molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) methods were applied to calculate binding free energies of APV to wild-type PR and these mutated PRs. The relative binding free energy differences from the TI calculations reveal that the decrease in van der Waals interactions of APV with mutated PRs relative to the wild-type PR mainly drives the drug resistance. This result is in good agreement with the previous experimental results and is also consistent with the results from MM-PBSA calculations. Analyses based on molecular dynamics trajectories show that these mutations can adjust the shape and conformation of the binding pocket, which provides main contributions to the decrease in the van der Waals interactions of APV with mutated PRs. The present study could provide important guidance for the design of new potent inhibitors that could alleviate drug resistance of PR due to mutations.