Multiple vaccines were developed and administered to immunize people worldwide against SARS-CoV-2 infection. However, changes in platelet count following the course of vaccination have been reported by many studies, suggesting vaccine-induced thrombocytopenia. In this context, designing an effective targeted subunit vaccine with high specificity and efficiency for people with low platelet counts has become a challenge for researchers. Using the in silico-based approaches and methods, the present study explored the antigenic epitopes of the spike protein of SARS-CoV-2 involved in initial binding of the virus with the angiotensin converting enzyme-2 receptor (ACE-2) on the respiratory epithelial cells. The top ten major histocompatibility complex-I (MHC-I) and MHC-II restricted epitopes were found to have 95.26% and 99.99% HLA-class-I population coverage, respectively. Among the top ten promiscuous MHC-I restricted epitopes, ’FTISVTTEI’ had the highest global HLA population coverage of 53.24%, with an antigenic score of 0.85 and a docking score of −162.4 Kcal/mol. The epitope ‘KLNDLCFTNV’ had the best antigenic score of 2.69 and an HLA population coverage of 43.4% globally. The study predicted and documented the most suitable epitopes with the widest global HLA coverage for synthesis of an efficient peptide-based vaccine against the deadly COVID-19.