Graphene is attractive for realizing optoelectronic devices, including photodetectors because of the unique advantages. It can easily co-work with other semiconductors to form a Schottky junction, in which the photo-carrier generated by light absorption in the semiconductor might be transported to the graphene layer efficiently by the build-in field. It changes the graphene conduction greatly and provides the possibility of realizing a graphene-based conductive-mode photodetector. Here we design and demonstrate a silicon-graphene conductive photodetector with improved responsivity and response speed. An electrical-circuit model is established and the graphene-sheet pattern is designed optimally for maximizing the responsivity. The fabricated silicon-graphene conductive photodetector shows a responsivity of up to ~105 A/W at room temperature (27 °C) and the response time is as short as ~30 μs. The temperature dependence of the silicon-graphene conductive photodetector is studied for the first time. It is shown that the silicon-graphene conductive photodetector has ultra-high responsivity when operating at low temperature, which provides the possibility to detect extremely weak optical power. For example, the device can detect an input optical power as low as 6.2 pW with the responsivity as high as 2.4 × 107 A/W when operating at -25 °C in our experiment.