2D van der Waals atomic crystal materials have great potential for use in future nanoscale electronic and optoelectronic applications owing to their unique properties such as a tunable energy band gap according to their thickness or number of layers. Recently, black phosphorous (BP) has attracted significant interest because it is a single-component material like graphene and has high mobility, a direct band gap, and exhibits ambipolar transition behavior. This study reports on a charge injection memory field-effect transistor on a glass substrate, where few-layer BPs act as the active channel and charge trapping layers, and Al2O3 films grown by atomic layer deposition act as the tunneling and blocking layers. Because of the ambipolar properties of BP nanosheets, both electrons and holes are involved in the charge trapping process, resulting in bilateral threshold voltage shifts with a large memory window of 22 V. Finally, a memory circuit of a resistive-load inverter is implemented that converts analog signals (current) to digital signals (voltage). Such a memory inverter also shows a clear memory window and distinct memory on/off switching characteristics.