Compared with traditional 3D bulk semiconductors, 2D layered semiconductors (e.g. transition metal dichalcogenides) have the features of large exciton binding energy, strong light-matter interaction and layer-dependent band structure, due to the intrinsic quantum confinement effect in the out-of-plane direction. Owing to such special photonic and photo-electronic properties, transition metal dichalcogenides and their van der Waals heterostructures have great potential for high-performance photodetector applications. In recent years, photodetector devices based on mechanisms such as photogating effect, photoconductive effect, photovoltaic effect, and photothermoelectric effect have been proposed and widely studied. Transition metal dichalcogenides planar optoelectronic devices based on photogating effect have similar device structures with transistors and compatible fabrication, together with high responsivity, but suffer from slow response speed and large dark current without applying gate bias, which limits the improvement of the device performance. Therefore, improving the response speed and reducing the dark current of transition metal dichalcogenides optoelectronic devices becomes an urgent issue.With mechanical exfoliation and dry transfer methods, van der Waals photodetectors with a graphene/MoS₂/h-BN/graphene vertical heterostructure are constructed (Fig.1). In the devices, MoS₂ performs as the photoabsorber with graphene as both top and bottom electrodes. The h-BN insulating layer is inserted between MoS₂ photoabsorber and the bottom graphene electrode as an effective and tunable barrier. Both AFM and Raman characterizations are taken to confirm the thickness of the materials and the device structures. The tunneling current from the top graphene electrode to the bottom graphene electrode through MoS₂ and h-BN under dark and laser illumination is measured with the home-built photocurrent measurement system. Based on the I-V characteristics of the vertical heterostructure device under both dark and laser illumination, together with the Fowler-Nordheim (FN) tunneling fitting of the I-V curves, the transport mechanism of FN tunneling is verified in the graphene/MoS₂/h-BN/graphene vertical heterostructure device (Fig.2). With the inserted wide bandgap h-BN insulating layer between the graphene electrode and MoS₂ photoabsorber, dark current was highly suppressed, while photogenerated carriers (holes in MoS₂) contributed effectively to the photocurrent through FN tunneling (Fig.3), which matches well with the observation of clear photocurrent when applying positive bias (Fig.2(b)). Detailed measurement of the photocurrent under laser illumination with various powers reveals the responsivity of the device of ~140 mA/W at laser power of 4.5 mW/cm² and I_light/I_dark ratio of ~2.3 at laser power of 41.4 mW/cm² (Fig.4) are achieved. A low dark current in the order of picoamperes and relatively high photodetection response speed with the response time of ~0.3 s are achieved, which is nearly two orders of magnitude higher than that of traditional graphene/MoS₂ heterostructure with the response time of ~20 s (Fig.5). The achieved low dark current and high response speed confirm the principle design of van der Waals vertical heterostructures based on FN tunneling effect in promoting the photodetection performance of the devices. A novel van der Waals vertical heterostructure with graphene/MoS₂/h-BN/graphene is developed to achieve high-performance photodetector properties with a low dark current and relatively high photodetection response speed, which verifies the significance of FN tunneling of photogenerated carriers for the development of van der Waals heterostructure photodetectors based on 2D materials.