We report on the discovery of HAT-P-38b, a Saturn-mass exoplanet, transiting the V = 12.56 dwarf star GSC 2314-00559 on a P = 4.6404 d circular orbit. The host star is a 0.89 M-circle dot late G dwarf, with solar metallicity and a radius of 0.92 R-circle dot. The planetary companion has a mass of 0.27 M-J and a radius of 0.82 R-J. HAT-P-38b is one of the planets the mass and radius of which have ever been discovered to be the closest to those of Saturn.