FRP (Fiber Reinforced Polymer) has been widely used in the reinforcement and renovation of existing concrete structures and new structures. FRP-constrained concrete columns are usually subjected to reciprocal cyclic action of axial pressure under seismic action, and it is important to study the stress-strain characteristics of FRP-constrained concrete under cyclic axial pressure for the application of FRP in practical engineering. In this paper, a neural network prediction model is proposed for modeling the stress-strain properties of FRP-confined concrete columns under cyclic axial pressure. The model uses long short-term memory (LSTM) units to model the hysteresis behaviors of cyclic stress-strain curves, and the physical parameters of the members are effectively integrated into the inputs of the network. The model can be efficiently trained in an end-to-end manner and does not rely on any expert experience. A cyclic axial pressure database containing 166 FRP-constrained plain concrete columns was produced, by means of which the accuracy and robustness of the model were fully evaluated. The results show that the average prediction error of the test set is only 0.32 MPa. In addition, the effects of network structure and hyperparameters were discussed in detail, and the results show that the model has excellent predictive performance.