The large photocurrent hysteresis observed in many organometal trihalide perovskite solar cells has become a major hindrance impairing the ultimate performance and stability of these devices, while its origin was unknown. Here we demonstrate the trap states on the surface and grain boundaries of the perovskite materials to be the origin of photocurrent hysteresis and that the fullerene layers deposited on perovskites can effectively passivate these charge trap states and eliminate the notorious photocurrent hysteresis. Fullerenes deposited on the top of the perovskites reduce the trap density by two orders of magnitude and double the power conversion efficiency of CH3NH3PbI3 solar cells. The elucidation of the origin of photocurrent hysteresis and its elimination by trap passivation in perovskite solar cells provides important directions for future enhancements to device efficiency.