An effective vaccine is needed to halt the spread of the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) pandemic. Recently, we reported safety, tolerability and antibody response data from an ongoing placebo-controlled, observer-blinded phase I/II coronavirus disease 2019 (COVID-19) vaccine trial with BNT162b1, a lipid nanoparticle-formulated nucleoside-modified mRNA that encodes the receptor binding domain (RBD) of the SARS-CoV-2 spike protein. Here we present antibody and T cell responses after vaccination with BNT162b1 from a second, non-randomized open-label phase I/II trial in healthy adults, 18-55 years of age. Two doses of 1-50 μg of BNT162b1 elicited robust CD4 and CD8 T cell responses and strong antibody responses, with RBD-binding IgG concentrations clearly above those seen in serum from a cohort of individuals who had recovered from COVID-19. Geometric mean titres of SARS-CoV-2 serum-neutralizing antibodies on day 43 were 0.7-fold (1-μg dose) to 3.5-fold (50-μg dose) those of the recovered individuals. Immune sera broadly neutralized pseudoviruses with diverse SARS-CoV-2 spike variants. Most participants had T helper type 1 (T1)-skewed T cell immune responses with RBD-specific CD8 and CD4 T cell expansion. Interferon-γ was produced by a large fraction of RBD-specific CD8 and CD4 T cells. The robust RBD-specific antibody, T cell and favourable cytokine responses induced by the BNT162b1 mRNA vaccine suggest that it has the potential to protect against COVID-19 through multiple beneficial mechanisms.