People living with HIV (PLWH) are at a higher risk of severe disease with SARS-CoV-2 virus infection. COVID-19 vaccines are effective in most PLWH. However, suboptimal immune responses to the standard two-shot regimen are a concern, especially for those with moderate to severe immunodeficiency. An additional dose is recommended as part of the extended primary series in Taiwan. Herein, we study the efficacy of this additional shot in PLWH with mild immunodeficiency compared to that in healthy non-HIV people. In total, 72 PLWH that were asymptomatic or with mild immunodeficiency (CD4 counts ≥200/mm3) and suppressed virology, and 362 healthcare workers of our hospital were enrolled. None of the participants had a history of SARS-CoV-2 infection. They received mRNA-1273 and ChAdOx1 vaccines. Anti-SARS-CoV-2 neutralizing and anti-Spike IgG antibodies, and SARS-CoV-2-specific T cell responses were evaluated. The standard two-shot regimen elicited lower responses in PLWH than the healthcare workers without HIV infection, although the difference was statistically insignificant. They had comparable levels of neutralizing and anti-Spike antibodies and comparable effector CD4+ and CD8+ T cell responses. The third shot boosted the SARS-CoV-2 immunity significantly more with better antibody responses and higher IFN-γ and IL-2 responses of the CD4+ and CD8+ T cells in PLWH compared to those without HIV. Upon in vitro stimulation with extracted Wuhan strain SARS-CoV-2 proteins, CD8+ T cells from PLWH after 3 shots had more durable effector responses than the non-HIV controls with extended time of stimulation. This subtle difference between PLWH and non-HIV people implied immune exhaustion with two shots in non-HIV people. Slightly compromised immunity in PLWH indeed preserved the functional capacity for further response to the third shot or natural infection.