Solar-blind photodetectors based on ultrawide bandgap semiconductors have attracted extensive attention due to their advantages such as ultra-low background noise and high chemical stability. In this work, for the first time we construct a high-performance avalanche photodetector (APD) based on the single crystalline ε-Ga2O3/BaSnO3 epitaxial heterojunction. The device exhibits a high rectification ratio of 106, and self-powered characteristics at zero bias, suggesting the formation of depletion region in ε-Ga2O3/BaSnO3 heterojunction. In addition, under a bias in the avalanche range, the APD presents avalanche multiplication behavior with a high responsivity of 1.5 × 104 A/W, and an ultrahigh gain of 1.6 × 106, which is the highest avalanche multiplication factor among reported Ga2O3-based heterojunction APDs. All these findings demonstrate that the designing of heterojunctions consisting of ε-Ga2O3 would provide a route to construct high performance optoelectronic devices.