A multilevel nonvolatile memory based on an amorphous indium–gallium–zinc oxide thin-film transistor is successfully demonstrated by using an atomic layer–deposited ZnO film as a charge trapping layer. The memory device shows a much higher erasing efficiency at a negative bias, i.e., after erasing at −13 V for 1 μs, the threshold voltage shift is as large as −7.4 V. In the case of 13 V/1 μs programming (P) and −12 V/1 μs erasing (E), the device demonstrates an ON/OFF readout drain current (IDS) ratio of ∼103 after 105 s, and a large and stable ON/OFF IDS ratio of ∼106 till 104 of P/E cycles. Furthermore, multilevel memory characteristics are also demonstrated on the device, showing an IDS ratio of >102 for 4 different states. Additionally, the device also successfully demonstrates typical synaptic behaviors, such as excitatory and inhibitory postsynaptic current with different memory times at different memory states.