We announce the discovery of GPX-1 b, a transiting brown dwarf with a mass of 19.7 +/- 1.6 M-Jup and a radius of 1.47 +/- 0.10 R-Jup, 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 +/- 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 M-circle dot, radius 1.56 +/- 0.10 R-circle dot, and approximate age 0.27(-0.15)(+0.09) Gyr. GPX-1 b has an orbital period of similar to 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.