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 1/2 coronavirus disease 2019 (COVID-19) vaccine trial with BNT162b1, a lipid nanoparticle (LNP) formulated nucleoside-modified messenger RNA (mRNA) encoding the receptor binding domain (RBD) of the SARS-CoV-2 spike protein1. Here we present antibody and T-cell responses after BNT162b1 vaccination from a second, non-randomized open-label phase 1/2 trial in healthy adults, 18-55 years of age. Two doses of 1 to 50 µg of BNT162b1 elicited robust CD4+ and CD8+ T-cell responses and strong antibody responses, with RBD-binding IgG concentrations clearly above those in a COVID-19 human convalescent sample (HCS) panel. Day 43 SARS-CoV-2 serum neutralising geometric mean titers were 0.7-fold (1 µg) to 3.5-fold (50 µg) those of the HCS panel. Immune sera broadly neutralised pseudoviruses with diverse SARS-CoV-2 spike variants. Most participants had T helper type 1 (TH1) skewed T cell immune responses with RBD-specific CD8+ and CD4+ T-cell expansion. Interferon (IFN)γ was produced by a high 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 multiple beneficial mechanisms with potential to protect against COVID-19.