This study used computer-based immunoinformatic analysis and the 3D structure of the SARS-CoV-2 spike protein to predict potential B-cell and T-cell epitopes for vaccine design. Nine conserved linear B-cell epitopes and multiple discontinuous B-cell epitopes composed of 69 surface residues were predicted. 62 T-cell epitopes were also predicted. Two mutations in a critical neutralizing epitope of SARS-CoV-2 may enable immune evasion. These predicted epitopes could inform peptide-driven vaccine design and serological diagnosis against COVID-19.