We announce the discovery of GPX-1 b, a transiting brown dwarf with a mass of 19.7 ± 1.6 MJup and a radius of 1.47 ± 0.10 RJup, the first substellar object discovered by the Galactic Plane eXoplanet (GPX) survey. The brown dwarf transits a moderately bright (V = 12.3 mag) fast-rotating F-type star with a projected rotational velocity $v\sin {\, i_*}=40\pm 10$ km s-1. We use the isochrone placement algorithm to characterize the host star, which has effective temperature 7000 ± 200 K, mass 1.68 ± 0.10 $\mathrm{\it M}_\odot$, radius 1.56 ± 0.10 $\mathrm{\it R}_\odot$, and approximate age $0.27_{-0.15}^{+0.09}$ Gyr. GPX-1 b has an orbital period of ~1.75 d and a transit depth of 0.90 ± 0.03 per cent. We describe the GPX transit detection observations, subsequent photometric and speckle-interferometric follow-up observations, and SOPHIE spectroscopic measurements, which allowed us to establish the presence of a substellar object around the host star. GPX-1 was observed at 30-min integrations by TESS in Sector 18, but the data are affected by blending with a 3.4 mag brighter star 42 arcsec away. GPX-1 b is one of about two dozen transiting brown dwarfs known to date, with a mass close to the theoretical brown dwarf/gas giant planet mass transition boundary. Since GPX-1 is a moderately bright and fast-rotating star, it can be followed-up by the means of the Doppler tomography.