A new flexible memory element is crucial for mobile and wearable electronics. A new concept for memory operation and innovative device structure with new materials is certainly required to address the bottleneck of memory applications now and in the future. We report a new nonvolatile molecular memory with a new operating mechanism based on two-dimensional (2D) material nanochannel field-effect transistors (FETs). The smallest channel length for our 2D material nanochannel FETs was approximately 30 nm. The modified molecular configuration for charge induced in the nanochannel of the MoS2 FET can be tuned by applying an up-gate voltage pulse, which can vary the channel conductance to exhibit memory states. Through controlling the amounts of triggered molecules through either different gate voltage pulses or gate duration time, multilevel states were obtained in the molecular memory. These new molecular memory transistors exhibited an erase/program ratio of more than three orders of current magnitude and high sensitivity, of a few picoamperes, at the current level. Reproducible operation and four-level states with stable retention and endurance were achieved. We believe this prototype device has potential for use in future memory devices.