The type I interferon (IFN-I)-inducible human restriction factor TRIM5α inhibits the infection of human cells by specific nonhuman retroviruses, such as N-MLV and EIAV, but does not generally target HIV-1. However, the introduction of two aminoacid substitutions, R332G and R355G, in the human TRIM5α (huTRIM5α) domain responsible for retroviral capsid recognition leads to efficient HIV-1 restriction upon stable over-expression. CRISPR-Cas-based approaches to precisely edit DNA could be employed to modify TRIM5 in human cells. Toward this aim, we used a DNA transfection-based CRISPR-Cas9 genome editing protocol to successfully mutate TRIM5 to its potentially HIV-1-restrictive version by homology-directed repair (HDR) in HEK293T cells. Nine clones bearing at least one HDR-edited TRIM5 allele containing both mutations were isolated (5.6% overall efficiency), whereas another one contained only the R332G mutation. Of concern, several of these HDR-edited clones contained on-target undesired mutations, and none had all the alleles corrected. Our study demonstrates the feasibility of editing the TRIM5 gene in human cells and identifies the main challenges to be addressed in order to use this approach to confer protection from HIV-1.