We developed a global peptide vaccine against SARS-CoV-2 that addresses the dual challenges of heterogeneity in the immune responses of different individuals and potential heterogeneity of the infecting virus. PolyPEPI-SCoV-2 is a polypeptide vaccine containing nine 30-mer peptides derived from all four major structural proteins of the SARS-CoV-2. Vaccine peptides were selected based on their frequency as HLA class I and class II personal epitopes (PEPIs) restricted to multiple autologous HLA alleles of individuals in an in silico cohort of 433 subjects of different ethnicities. PolyPEPI-SCoV-2 vaccine administered with Montanide ISA 51VG adjuvant generated robust, Th1-biased CD8+ and CD4+ T cell responses against all four structural proteins of the virus, as well as binding antibodies upon subcutaneous injection into BALB/c and CD34+ transgenic mice. In addition, PolyPEPI-SCoV-2-specific, polyfunctional CD8+ and CD4+ T cells were detected ex vivo in each of the 17 asymptomatic/mild COVID-19 convalescents' blood investigated, 1-5 months after symptom onset. The PolyPEPI-SCoV-2-specific T cell repertoire used for recovery from COVID-19 was extremely diverse: donors had an average of seven different peptide-specific T cells, against the SARS-CoV-2 proteins, 87% of donors had multiple targets against at least three SARS-CoV-2 proteins and 53% against all four. In addition, PEPIs determined based on the complete HLA class I genotype of the convalescent donors were validated, with 84% accuracy, to predict PEPI-specific CD8+ T cell responses measured for the individuals. Extrapolation of the above findings to a US bone marrow donor cohort of 16,000 HLA-genotyped individuals with 16 different ethnicities (n=1,000 each ethnic group) suggest that PolyPEPI-SCoV-2 vaccination in a general population will likely elicit broad, multi-antigenic CD8+ and CD4+ T cell responses in 98% of individuals, independent of ethnicity, including Black, Asian, and Minority Ethnic (BAME) cohorts.