InSb nanocrystals (NCs) have shown promising applications in various areas. In this work, we have synthesized high-quality InSb NCs on Si-based substrates via a self-catalyzed chemical vapor deposition (CVD) method. Compared with the InSb NCs synthesis methods reported before, the one presented here is more facile, cost-effective, and compatible with the state-of-the-art Si-based microelectronic processing. By controlling the thickness of the pre-evaporated indium layer and the growth time, we can obtain NCs with diameters ranging from 54 to 182 nm. The NCs are single crystalline with stoichiometric element ratio. We also fabricate near-infrared photodetectors with the hybrid structure of graphene and InSb NCs. The CVD-grown large-scale graphene benefits the device application. Under 1550 nm laser illumination, the photodetectors with smaller NCs exhibit better photoresponse behavior, the responsivity of which can be as high as 195 A W⁻¹, higher than those of most reported graphene-based 1550 nm photodetectors. The physical mechanism for the high responsivity feature of this kind of device is discussed.