SARS-CoV-2 causes COVID-19, urgently requiring the development of effective vaccine(s). Much of current efforts focus on the SARS-CoV-2 spike-glycoprotein by identifying highly antigenic epitopes as good vaccine candidates. However, high antigenicity is not sufficient, since the activation of relevant T cells depends on the presence of the complex of the antigen with a suitably matching Human Leukocyte Antigen (HLA) Class II molecule, not the antigen alone: in the absence of such a match, even a highly antigenic epitope in vitro will not elicit antibody formation in vivo. Here we assessed systematically in silico the binding affinity of epitopes of the spike-glycoprotein to 66 common HLA-Class-II alleles (frequency ≥ 0.01). We used a sliding epitope window of 22-amino-acid-width to scan the entire protein and determined the binding affinity of each subsequence to each HLA allele. DPB1 had highest binding affinities, followed by DRB1 and DQB1. Higher binding affinities were concentrated in the initial part of the glycoprotein (S1-S460), with a peak at S223-S238. This region would be well suited for effective vaccine development by ensuring high probability for successful matching of the vaccine antigen from that region to a HLA Class II molecule for CD4 T cell activation by the antigen-HLA molecule complex.