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We announce the discovery of GPX-1 b, a transiting brown dwarf with a mass of $19.7\pm 1.6$ $M_{\mathrm{Jup}}$ and a radius of $1.47\pm0.10$ $R_{\mathrm{Jup}}$, the first sub-stellar 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 $v\sin{ i_*}=40\pm10$ km/s. We use the isochrone placement algorithm to characterize the host star, which has effective temperature $7000\pm200$ K, mass $1.68\pm0.10$ $M_{\mathrm{Sun}}$, radius $1.56\pm0.10$ $R_{\mathrm{Sun}}$ and approximate age $0.27_{-0.15}^{+0.09}$ Gyr. GPX-1 b has an orbital period of $\sim$1.75 d, and a transit depth of $0.90\pm0.03$ %. 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 sub-stellar object around the host star. GPX-1 was observed at 30-min integrations by TESS in Sector 18, but the data is 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 Doppler tomography.