We assessed a cohort of people living with human immunodeficiency virus (PLWH) (n = 110) and HIV negative controls (n = 64) after 1, 2 or 3 SARS-CoV-2 vaccine doses. At all timepoints, PLWH had significantly lower neutralizing antibody (nAb) titers than HIV-negative controls. We also observed a delayed development of neutralization in PLWH that was underpinned by a reduced frequency of spike-specific memory B cells (MBCs). Improved neutralization breadth was seen against the Omicron variant (BA.1) after the third vaccine dose in PLWH but lower nAb responses persisted and were associated with global MBC dysfunction. In contrast, SARS-CoV-2 vaccination induced robust T cell responses that cross-recognized variants in PLWH. Strikingly, individuals with low or absent neutralization had detectable functional T cell responses. These PLWH had reduced numbers of circulating T follicular helper cells and an enriched population of CXCR3+CD127+CD8+T cells after two doses of SARS-CoV-2 vaccination.