A novel severe acute respiratory syndrome human coronavirus (SARS HCoV) was identified from respiratory illness patients (named SARS-CoV-2 by ICTV) in December 2019 and has recently emerged as a serious threat to world public health. However, no approved drugs have been found to effectively inhibit the virus. Since it has been reported that HIV protease inhibitors can be used as anti-SARS drugs by targeting SARS-CoV-1 3CLpro, we chose six approved anti-HIV drugs and investigated their binding interactions with 3CLpro to evaluate their potential to become clinical drugs for the new coronavirus pneumonia (COVID-19) caused by SARS-CoV-2 infection. The molecular docking results indicate that the 3CLpro of SARS-CoV-2 has a higher binding affinity for all the studied inhibitors than does SARS-CoV-1. Two docking complexes (indinavir and darunavir) with high docking scores were further subjected to MM-PBSA binding free energy calculations to detail the molecular interactions between these two protease inhibitors and SARS HCoV 3CLpro. Our results show that, among the inhibitors tested, darunavir has the highest binding affinity with SARS-CoV-2 and SARS-CoV-1 3CLpro, indicating that it may have the potential to be used as an anti-COVID-19 clinical drug. The mechanism behind the increased binding affinity of HIV protease inhibitors toward SARS-CoV-2 3CLpro (as compared to SARS-CoV-1) was investigated by MD simulations. Our study provides insight into the possible role of structural flexibility during interactions between SARS HCoV 3CLpro and inhibitors and sheds light on structure-based design of anti-COVID-19 drugs targeting SARS-CoV-2 3CLpro.