Recently, two-dimensional materials such as molybdenum disulphide (MoS2) have been demonstrated to realize field effect transistors (FET) with a large current on-off ratio. However, the carrier mobility in backgate MoS2 FET is rather low (typically 0.5-20 cm(2)/V · s). Here, we report a novel field-effect Schottky barrier transistors (FESBT) based on graphene-MoS2 heterojunction (GMH), where the characteristics of high mobility from graphene and high on-off ratio from MoS2 are properly balanced in the novel transistors. Large modulation on the device current (on/off ratio of 10(5)) is achieved by adjusting the backgate (through 300 nm SiO2) voltage to modulate the graphene-MoS2 Schottky barrier. Moreover, the field effective mobility of the FESBT is up to 58.7 cm(2)/V · s. Our theoretical analysis shows that if the thickness of oxide is further reduced, a subthreshold swing (SS) of 40 mV/decade can be maintained within three orders of drain current at room temperature. This provides an opportunity to overcome the limitation of 60 mV/decade for conventional CMOS devices. The FESBT implemented with a high on-off ratio, a relatively high mobility and a low subthreshold promises low-voltage and low-power applications for future electronics.