Atomically thin MoS2 film has displayed great potential for future optoelectronics due to its outstanding photonic and electronic properties. However, many important applications, especially for photodetection, are still severely limited by its low light absorption. In this paper, we demonstrate a high-performance photodetector based on perovskite/MoS2 hybrid film, which exhibits sensitive, fast, and stable response under low operation potential. The external photoresponsivity is about 342 A/W at bias potential of 2 V without gate voltage under incident power of 2.2 pW (520 nm), which is superior than most of the photodetectors based on transition metal dichalcogenides and perovskite. The devices show high stability during transient on/off test without any encapsulation, in which the response and recovery time has been recorded as 27 ms and 21 ms, respectively. Besides, the devices can be fabricated on various substrates, including SiO2/Si, transparent glass and flexible PET, etc. The flexible perovskite/MoS2 photodetectors with ultrahigh stability during 20,000 times bending was reported for the first time. We expect the proposed hybrid photodetector would be a competitive candidate in future flexible electronics. Our research also paves the way to integrate various atomically thin films with highly optical absorption materials.