We demonstrate room-temperature ferroelectric field-effect transistors (Fe-FETs) with MoS2 and CuInP2S6 two-dimensional (2D) van der Waals heterostructure. The ferroelectric CuInP2S6 is a 2D ferroelectric insulator, integrated on top of MoS2 channel providing a 2D/2D semiconductor/insulator interface without dangling bonds. The MoS2- and CuInP2S6-based 2D van der Waals heterostructure Fe-FETs exhibit a clear counterclockwise hysteresis loop in transfer characteristics, demonstrating their ferroelectric properties. This stable nonvolatile memory property can also be modulated by the back-gate bias of the MoS2 transistors because of the tuning of capacitance matching between the MoS2 channel and the ferroelectric CuInP2S6, leading to the enhancement of the on/off current ratio. Meanwhile, the CuInP2S6 thin film also shows resistive switching characteristics with more than four orders of on/off ratio between low- and high-resistance states, which is also promising for resistive random-access memory applications.