Hybrid organic-inorganic (HOI) photodiodes have both advantages of organic and inorganic materials, including compatibility of traditional Si-based semiconductor technology, low cost, high photosensitivity and high reliability, showing tremendous value in application. Red light sensitive HOI photodiodes based on the p-Si/copper phthalocyanine (CuPc) hetrojunction were fabricated and characterized. The effects of CuPc layer thickness on the performance were investigated, and an optimal layer thickness of around 30 nm was determined. An analytical expression is derived to describe the measured thickness dependence of the saturation photocurrent. For the device with optimal CuPc layer thickness, a photoresponsivity of 0.35 A/W and external quantum efficiency of 70% were obtained at 9 V reverse voltage bias and 655 nm light illumination of 0.451 mW. Furthermore, optical power dependent performances were investigated.