2D transition metal dichalcogenides are emerging with tremendous potential in many optoelectronic applications due to their strong light-matter interactions. To fully explore their potential in photoconductive detectors, high responsivity is required. Here, high responsivity phototransistors based on few-layer rhenium disulfide (ReS2) are presented. Depending on the back gate voltage, source drain bias and incident optical light intensity, the maximum attainable photoresponsivity can reach as high as 88 600 A W-1, which is a record value compared to other individual 2D materials with similar device structures and two orders of magnitude higher than that of monolayer MoS2. Such high photoresponsivity is attributed to the increased light absorption as well as the gain enhancement due to the existence of trap states in the few-layer ReS2 flakes. It further enables the detection of weak signals, as successfully demonstrated with weak light sources including a lighter and limited fluorescent lighting. Our studies underscore ReS2 as a promising material for future sensitive optoelectronic applications.