Graphene-based photodetectors exhibit relatively low spectral absorption and rapid recombination of photogenerated carriers, which can limit their response performance. On the other hand, nanostructured lead sulfide (PbS) demonstrates a wide spectral absorption range from visible to near-infrared light. High-quality and evenly distributed PbS nanofilms were synthesized by chemical bath deposition and were applied to a graphene-PbS heterostructure photodetector. The heterostructure creates an inherent electric field that extends the lifetime of photogenerated carriers, leading to enhanced device response. We achieved a high-responsivity graphene-PbS photodetector by combining the high carrier mobility of graphene and the strong infrared absorption of PbS. The photodetector exhibits a responsivity of 72 A/W at 792 nm and 5.8 A/W at 1550 nm, with a response time of less than 20 ms. The optimized device features a broad spectral response ranging from 265 nm to 2200 nm.