The HIV-1 capsid protein makes up the core of the virion and plays a critical role in early steps of HIV replication. Due to its exposure in the cytoplasm after entry, HIV capsid is a target for host cell factors that act directly to block infection such as TRIM5alpha and MxB. Several host proteins also play a role in facilitating infection, including in the protection of HIV-1 capsid from recognition by host cell restriction factors. Through an unbiased screening approach, called HIV-CRISPR, we show that the CPSF6-binding deficient, N74D HIV-1 capsid mutant is sensitive to restriction mediated by human TRIM34, a close paralog of the well-characterized HIV restriction factor TRIM5alpha. This restriction occurs at the step of reverse transcription, is independent of interferon stimulation, and limits HIV-1 infection in key target cells of HIV infection including CD4+ T cells and monocyte-derived dendritic cells. TRIM34 can also restrict some SIV capsids. TRIM34 restriction requires TRIM5alpha as knockout or knockdown of TRIM5alpha results in a loss of antiviral activity. Through immunofluorescence studies, we show that TRIM34 and TRIM5alpha colocalize to cytoplasmic bodies and are more frequently observed to be associated with infecting N74D capsids than with WT HIV-1 capsids. Our results identify TRIM34 as an HIV-1 CA-targeting restriction factor and highlight the potential role for heteromultimeric TRIM interactions in contributing to restriction of HIV-1 infection in human cells.