The use of two-dimensional materials and van der Waals heterostructures holds great potential for improving the performance of memristors Here, we present SnS2/MoTe2 heterostructure synaptic transistors. Benefiting from the ultra-low dark current of the heterojunction, the power consumption of the synapse is only 19 pJ per switching under 0.1 V bias, comparable to that of biological synapses. The synaptic device based on the SnS2/MoTe2 demonstrates various synaptic functionalities, including short-term plasticity, long-term plasticity, and paired-pulse facilitation (PPF). In particular, the synaptic weight of the excitatory postsynaptic current (EPSC) can reach 109.8%. In addition, the controllability of the long-term potentiation (LTP) and long-term depression (LTD) are discussed. The dynamic range (Gmax/Gmin) and the symmetricity values of the synaptic devices are approximately 16.22 and 6.37, and the non-linearity is 1.79. Our study provides the possibility for the application of 2D material synaptic devices in the field of low-power information storage.