We report the discovery of a planetary system orbiting TOI-763(aka CD-39 7945), a V = 10.2, high proper motion G-type dwarf star that was photometrically monitored by the TESS space mission in Sector 10. We obtain and model the stellar spectrum and find an object slightly smaller than the Sun, and somewhat older, but with a similar metallicity. Two planet candidates were found in the light curve to be transiting the star. Combining TESS transit photometry with HARPS high-precision radial velocity (RV) follow-up measurements confirm the planetary nature of these transit signals. We determine masses, radii, and bulk densities of these two planets. A third planet candidate was discovered serendipitously in the RV data. The inner transiting planet, TOI-763 b, has an orbital period of Pb = 5.6 d, a mass of Mb = 9.8 ± 0.8 M⊕, and a radius of Rb = 2.37 ± 0.10 R⊕. The second transiting planet, TOI-763 c, has an orbital period of Pc = 12.3 d, a mass of Mc = 9.3 ± 1.0 M⊕, and a radius of Rc = 2.87 ± 0.11 R⊕. We find the outermost planet candidate to orbit the star with a period of ∼48 d. If confirmed as a planet, it would have a minimum mass of Md = 9.5 ± 1.6 M⊕. We investigated the TESS light curve in order to search for a mono transit by planet d without success. We discuss the importance and implications of this planetary system in terms of the geometrical arrangements of planets orbiting G-type stars.