Weak light absorption of graphene has limited the responsivity of graphene-based photodetectors. On the other hand, the slow response of PbSe as a mid-infrared range (MIR) detector makes this type of detector unsuitable as a commercial detector. Here, we report a fast MIR detector based on hybrid graphene-PbSe nanorods. For this purpose, a few-layer graphene piece was synthesized using a simple, scalable, and economical method on a cobalt layer, the synthesized graphene was transferred onto interdigitated copper electrodes, and then synthesized nanorods were spin coated on the transferred graphene. Strong and tunable light absorption in the quantum dot layer creates electric charges, which are transferred to the graphene, and due to the high charge mobility of graphene and long trapped-charge lifetimes in the quantum dot layer, they recirculate many times. The fabricated device has high speed and responsivity. The gain of fabricated detectors based on hybrid graphene quantum dots is 10.3 times more, their response time is 14.3 times faster, and their responsivity is 10 times more than conventional nanorod-based detectors. From the point of view of spectral selectivity, tuning the size of the nanorods helps optical detection from the IR to mid-IR.