Acquired immunodeficiency syndrome (AIDS) has been a chronic, life-threatening disease for a long time. Though, a broad range of antiretroviral drug regimens is applicable for the successful suppression of virus replication in human immunodeficiency virus type 1 (HIV-1) infected people. The mutation-induced drug resistance problems during the treatment of AIDS forced people to continuously look for new antiviral agents. HIV-1 integrase (IN) and reverse transcriptase associated ribonuclease (RT-RNase H), two pivotal enzymes in HIV-1 replication progress, have gained popularity as druggable targets for designing novel HIV-1 antiviral drugs. During the development of HIV-1 IN and/or RT-RNase H inhibitors, computer-aided drug design (CADD), including homology modeling, pharmacophore, docking, molecular dynamics (MD) simulation and binding free energy calculation, represent a significant tool to accelerate the discovery of new drug candidates and reduce costs in antiviral drug development. In this review, we summarized the recent advances in the design of single- and dual-target inhibitors against HIV-1 IN or/and RT-RNase H as well as the prediction of mutation-induced drug resistance based on computational methods. We highlighted the results of the reported literatures and proposed some perspectives on the design of novel and more effective antiviral drugs in the future.