The SARS-CoV-2 pandemic has created a public health crisis worldwide. Although vaccines against the virus are efficiently being rolled out, they are proving to be ineffective against certain emerging SARS-CoV-2 variants. The high degree of sequence similarity between SARS-CoV-2 and other human coronaviruses (HCoV) presents the opportunity for designing vaccines that may offer protection against SARS-CoV-2 and its emerging variants, with cross-protection against other HCoVs. In this study, we performed bioinformatics analyses to identify T and B cell epitopes originating from spike, membrane, nucleocapsid, and envelope protein sequences found to be evolutionarily conserved among seven major HCoVs. Evolutionary conservation of these epitopes indicates that they may have critical roles in viral fitness and are, therefore, unlikely to mutate during viral replication thus making such epitopes attractive candidates for a vaccine. Our designed vaccine construct comprises of twelve T and six B cell epitopes that are conserved among HCoVs. The vaccine is predicted to be soluble in water, stable, have a relatively long half-life, and exhibit low allergenicity and toxicity. Our docking results showed that the vaccine forms stable complex with toll-like receptor 4, while the immune simulations predicted that the vaccine may elicit strong IgG, IgM, and cytotoxic T cell responses. Therefore, from multiple perspectives, our multi-subunit vaccine design shows the potential to elicit a strong immune-protective response against SARS-CoV-2 and its emerging variants while carrying minimal risk for causing adverse effects.