This Letter demonstrates the capability of long short term memory (LSTM) network in capturing the complex hysteretic dynamics in piezoelectric actuators (PEAs). A LSTM network is constructed to model the PEAs' complex dynamics, which includes static hysteresis, creep, high-order dynamics. The network is trained and evaluated by data sets of input–output pairs with different frequencies and amplitudes. Preliminary results show that, even for the simplest topology, namely one layer with one cell, the LSTM network provides a satisfactory precision in a wide frequency range. Thus, LSTM networks may provide a new approach to approximate the dynamics in complex engineering systems.