Simple stacking of thin van der Waals 2D materials with different physical properties enables one to create heterojunctions (HJs) with novel functionalities and new potential applications. Here, a 2D material p-n HJ of GeSe/MoS2 is fabricated and its vertical and horizontal carrier transport and photoresponse properties are studied. Substantial rectification with a very high contrast (>10(4)) through the potential barrier in the vertical-direction tunneling of HJs is observed. The negative differential transconductance with high peak-to-valley ratio (>10(5)) due to the series resistance change of GeSe, MoS2, and HJs at different gate voltages is observed. Moreover, strong and broad-band photoresponse via the photoconductive effect are also demonstrated. The explored multifunctional properties of the GeSe/MoS2 HJs are expected to be important for understanding the carrier transport and photoresponse of 2D-material HJs for achieving their use in various new applications in the electronics and optoelectronics fields.