We investigated the trap-mediated electronic transport properties of pentacene/molybdenum disulphide (MoS2) p-n heterojunction devices. We observed that the hybrid p-n heterojunctions were gate-tunable and were strongly affected by trap-assisted tunnelling through the van der Waals gap at the heterojunction interfaces between MoS2 and pentacene. The pentacene/MoS2 p-n heterojunction diodes had gate-tunable high ideality factor, which resulted from trap-mediated conduction nature of devices. From the temperature-variable current-voltage measurement, a space-charge-limited conduction and a variable range hopping conduction at a low temperature were suggested as the gate-tunable charge transport characteristics of these hybrid p-n heterojunctions. Our study provides a better understanding of the trap-mediated electronic transport properties in organic/2-dimensional material hybrid heterojunction devices.