Combinational antiretroviral therapy (cART) suppresses human immunodeficiency virus type 1 (HIV-1) viral replication and pathogenesis in acquired immunodeficiency syndrome (AIDS) patients. However, HIV-1 remains in the latent stage of infection by suppressing viral transcription, which hinders an HIV-1 cure. One approach for an HIV-1 cure is the "shock and kill" strategy. The strategy focuses on reactivating latent HIV-1, inducing the viral cytopathic effect and facilitating the immune clearance for the elimination of latent HIV-1 reservoirs. Here, we reported that the H3K4 trimethylation (H3K4me3)-specific demethylase KDM5A/B play a role in suppressing HIV-1 Tat/LTR-mediated viral transcription in HIV-1 latent cells. Furthermore, we evaluated the potential of KDM5-specific inhibitor JQKD82 as an HIV-1 "shock and kill" agent. Our results showed that JQKD82 increases the H3K4me3 level at HIV-1 5' LTR promoter regions, HIV-1 reactivation, and the cytopathic effects in an HIV-1-latent T cell model. In addition, we identified that the combination of JQKD82 and AZD5582, a non-canonical NF-κB activator, generates a synergistic impact on inducing HIV-1 lytic reactivation and cell death in the T cell. The latency-reversing potency of the JQKD82 and AZD5582 pair was also confirmed in peripheral blood mononuclear cells (PBMCs) isolated from HIV-1 aviremic patients and in an HIV-1 latent monocyte. In latently infected microglia (HC69) of the brain, either deletion or inhibition of KDM5A/B results in a reversal of the HIV-1 latency. Overall, we concluded that KDM5A/B function as a host repressor of the HIV-1 lytic reactivation and thus promote the latency and the survival of HIV-1 infected reservoirs.