Two-dimensional layered transition-metal dichalcogenides have attracted considerable interest for their unique layer-number-dependent properties. In particular, vertical integration of these two-dimensional crystals to form van der Waals heterostructures can open up a new dimension for the design of functional electronic and optoelectronic devices. Here we report the layer-number-dependent photocurrent generation in graphene/MoS2/graphene heterostructures by creating a device with two distinct regions containing one-layer and seven-layer MoS2 to exclude other extrinsic factors. Photoresponse studies reveal that photoresponsivity in one-layer MoS2 is surprisingly higher than that in seven-layer MoS2 by seven times. Spectral-dependent studies further show that the internal quantum efficiency in one-layer MoS2 can reach a maximum of 65%, far higher than the 7% in seven-layer MoS2. Our theoretical modelling shows that asymmetric potential barriers in the top and bottom interfaces of the graphene/one-layer MoS2/graphene heterojunction enable asymmetric carrier tunnelling, to generate usually high photoresponsivity in one-layer MoS2 device.