Photodetectors based on PbSe quantum dots (QDs) are commonly used for light detection in the near-infrared (NIR) region. Nevertheless, the performance of photodetectors based on PbSe QDs is constrained by ineffective carrier transfer and poor photo and thermal stabilities. Herein, a promising strategy that harnesses PbSe/PbS core/shell QDs structures is developed and demonstrated to enhance the long-term stability of photodetectors, further combining with graphene to form hybrid heterojunctions that effectively promote carrier transfer. As a result, the devices exhibit a broad photoresponse to the incident light at range of 365–1250 nm, and also possess a high photosensitivity of 1.5 × 104 A/W and a high detectivity of 4.0 × 1013 Jones. Moreover, the lifetime of graphene-PbSe/PbS core/shell QDs hybrid photodetector was 9 times greater than that of uncoated QDs devices. The enormous boost might be attributed to the passivation and protection provided by the core–shell structure, and graphene’s efficient extraction of charge carriers.