The two-dimensional/three-dimensional van der Waals heterostructures provide novel optoelectronic properties for the next-generation of information devices. Herein, MoS2/Ge heterojunction avalanche photodetectors are readily obtained. The device with an Ag electrode at MoS2 side exhibits more stable rectification characteristics than that with an Au electrode. The rectification radio greater than 103 and a significant avalanche breakdown are observed in the device. The responsivity of 170 and 4 A/W and the maximum gain of 320 and 13 are obtained under 532 and 1550 nm illumination, respectively. Such photoelectric properties are attributed to the carrier multiplication at a Ge/MoS2 junction due to an avalanche breakdown. The mechanism is confirmed by the Sentaurus TCAD-simulated I-V characteristics.