The prediction for chaotic trajectory from the measured data of time history, without prior knowledge of underlying dynamical model, is a challenging task in the data-driven analysis, due to its sensitivity to initial conditions. In this paper, the Long Short-Term Memory Network (LSTM) with the merge layer is proposed to predict the future states of the coupled Morris-Lecar (M-L) system with the chaotic itinerancy responses. Here, the two LSTM models with single-branch and multi-branch are constructed respectively to carry out the predictions in the multivariate loading conditions. By comparison to the network model with single-branch, the multi-branch model with adding merge layer can provide a high utilization of weights to reduce training cost greatly and receive a low prediction error, which make the multi-layer LSTM promising to estimate a high-dimensional complex dynamical behavior like transient chaotic itinerancy.