As a unique perovskite transparent oxide semiconductor, high-mobility La-doped BaSnO3 films have been successfully synthesized by molecular beam epitaxy and pulsed laser deposition. However, it remains a big challenge for magnetron sputtering, a widely applied technique suitable for large-scale fabrication, to grow high-mobility La-doped BaSnO3 films. Here, we developed a method to synthesize high-mobility epitaxial La-doped BaSnO3 films (mobility up to 121 cm2V-1s-1 at the carrier density ~ 4.0 x 10^20 cm-3 at room temperature) directly on SrTiO3 single crystal substrates using high-pressure magnetron sputtering. The structural and electrical properties of the La-doped BaSnO3 films were characterized by combined high-resolution X-ray diffraction, X-ray photoemission spectroscopy, and temperature-dependent electrical transport measurements. The room temperature electron mobility of La-doped BaSnO3 films in this work is 2 to 4 times higher than the reported values of the films grown by magnetron sputtering. Moreover, in the high carrier density range (n > 3 x 10^20 cm-3), the electron mobility value of 121 cm2V-1s-1 in our work is among the highest values for all reported doped BaSnO3 films. It is revealed that high argon pressure during sputtering plays a vital role in stabilizing the fully relaxed films and inducing oxygen vacancies, which benefit the high mobility at room temperature. Our work provides an easy and economical way to massively synthesize high-mobility transparent conducting films for transparent electronics.