The presence of latent human immunodeficiency virus (HIV) reservoirs is a major obstacle to a cure. The “shock and kill” therapy is based on the concept that latent reservoirs in HIV carriers with antiretroviral therapy are reactivated by latency-reversing agents (LRAs), followed by elimination due to HIV-associated cell death or killing by virus-specific cytotoxic T lymphocytes. Protein kinase C (PKC) activators are considered robust LRAs as they efficiently reactivate latently infected HIV. However, various adverse events hamper the intervention trial of PKC activators as LRAs. We found in this study that a novel PKC activator, 10-Methyl-aplog-1 (10MA-1), combined with an inhibitor of bromodomain and extra-terminal domain motifs, JQ1, strongly and synergistically reactivated latently infected HIV. Notably, higher concentrations of 10MA-1 alone induced the predominant side effect, i.e., global T cell activation as defined by CD25 expression and pro-inflammatory cytokine production in primary CD4+ T lymphocytes; however, JQ1 efficiently suppressed the 10MA-1-induced side effect in a dose-dependent manner. Considering the reasonable accessibility and availability of 10MA-1 since the chemical synthesis of 10MA-1 requires fewer processes than that of bryostatin 1 or prostratin, our results suggest that the combination of 10MA-1 with JQ1 may be a promising pair of LRAs for the clinical application of the “shock and kill” therapy.