Highly purified semiconducting carbon nanotube (CNT) thin films and graphene are used to fabricate hybrid photodetector. The results indicate that the hot carriers generated in graphene can tunnel into bottom CNT film through nanometer thick silicon film when illuminated. As a result, electrons and holes are accumulated at separated side of the silicon layer, resulting in a modulation of the current in the CNT film transistor due to the photogating effect. The photodetector shows a responsivity of 83 mA/W for visible light (633 nm) and a good response within the near-infrared range. Such CNT film-graphene photodetector, taking advantages of both broadband absorption of graphene and small dark current of semiconducting CNTs, paves the way to future high performance infrared photodetectors.