We explored the possibility of producing a high-mobility two-dimensional electron gas (2DEG) in the LaAlO3/SrGeO3 and LaGaO3/BaSnO3 heterostructures using first-principles electronic structure calculations. Our results show that the 2DEG occurs at n-type LaAlO3/SrGeO3 and LaGaO3/BaSnO3 interfaces. Compared to the prototype LaAlO3/SrTiO3, LaAlO3/SrGeO3 and LaGaO3/BaSnO3 systems yield comparable total interfacial charge carrier density but much lower electron effective mass (nearly half the value of LaAlO3/SrTiO3), thus resulting in about twice larger electron mobility and enhanced interfacial conductivity. This work demonstrates that SrGeO3 and BaSnO3 can be potential substrate materials to achieve a high-mobility 2DEG in the perovskite-oxide heterostructures.