We discovered that perovskite (Ba,La)SnO3 can have excellent carrier mobility even though its band gap is large. The Hall mobility of Ba0.98La0.02SnO3 crystals with the n-type carrier concentration of sim 8-10times10 19 cm-3 is found to be sim 103 cm2 V-1s-1 at room temperature, and the precise measurement of the band gap Delta of a BaSnO3 crystal shows Delta=4.05 eV, which is significantly larger than those of other transparent conductive oxides. The high mobility with a wide band gap indicates that (Ba,La)SnO3 is a promising candidate for transparent conductor applications and also epitaxial all-perovskite multilayer devices.