Abstract Distant quasars are unique tracers to study the formation of the earliest supermassive black holes (SMBHs) and the history of cosmic reionization. Despite extensive efforts, only two quasars have been found at z ≥ 7.5, due to a combination of their low spatial density and the high contamination rate in quasar selection. We report the discovery of a luminous quasar at z = 7.642, J0313−1806, the most distant quasar yet known. This quasar has a bolometric luminosity of 3.6 × 1013 L ⊙. Deep spectroscopic observations reveal a SMBH with a mass of (1.6 ± 0.4) × 109 M ⊙ in this quasar. The existence of such a massive SMBH just ∼670 million years after the big bang challenges significantly theoretical models of SMBH growth. In addition, the quasar spectrum exhibits strong broad absorption line (BAL) features in C iv and Si iv, with a maximum velocity close to 20% of the speed of light. The relativistic BAL features, combined with a strongly blueshifted C iv emission line, indicate that there is a strong active galactic nucleus (AGN)-driven outflow in this system. Atacama Large Millimeter/submillimeter Array observations detect the dust continuum and [C ii] emission from the quasar host galaxy, yielding an accurate redshift of 7.6423 ± 0.0013 and suggesting that the quasar is hosted by an intensely star-forming galaxy, with a star formation rate of ∼200 M ⊙ yr−1 and a dust mass of ∼7 × 107 M ⊙. Follow-up observations of this reionization-era BAL quasar will provide a powerful probe of the effects of AGN feedback on the growth of the earliest massive galaxies.