The extensive utilisation of antiretroviral therapy has greatly improved the survival rates of those infected with human immunodeficiency virus (HIV). The objective of this study was to compare 3-drug regimens containing non-nucleoside reverse transcriptase inhibitor with 3-drug regimens containing integrase inhibitor (INI) regarding efficacy and safety in treatment-naive HIV-1-infected adults at 48 and 96 weeks, respectively. This study was a network meta-analysis using a Bayesian methodology. On January 8, 2020, we searched databases and other sources for randomized controlled trials conducted in treatment-naive HIV-1 adults and compared multiple 3-drug antiretroviral regimens containing INI, efavirenz (EFV), or rilpivirine (RPV). We extracted data on the following outcomes: virologic suppression, CD4 cell recovery, discontinuations, deaths, adverse events, serious adverse events, deaths related to study drugs, and drug-related adverse events. We conducted calculations within a Bayesian framework using R software. The network contained 15 randomized controlled trials including 9,745 patients. For efficacy outcomes, regimens containing INI, especially dolutegravir (DTG), were generally superior to other regimens. For virologic suppression at 48 weeks, odds ratios (95% credible intervals) were 0.6 (0.43, 0.82) for EFV+ tenofovir disoproxil fumarate (TDF)+emtricitabine (FTC) versus DTG+ abacavir+ lamivudine (3TC) and 0.52 (0.36, 0.75) for EFV+TDF+FTC vs. DTG+TDF+FTC/3TC. For safety outcomes, regimens containing INI tended to be safer relative to regimens without INI. Outcomes associated with death were unsuitable for network meta-analysis due to low event rates. 3-drug regimens containing INI demonstrate better efficacy and safety than those containing RPV or EFV.