A solid oxide fuel cell (SOFC) system is a kind of green chemical-energy–electric-energy conversion equipment with broad application prospects. In order to ensure the long-term stable operation of the SOFC power-generation system, prediction and evaluation of the system’s operating state are required. The mechanism of the SOFC system has not been fully revealed, and data-driven single-step prediction is of little value for practical applications. The state-prediction problem can be regarded as a time series prediction problem. Therefore, an innovative deep learning model for SOFC system state prediction is proposed in this study. The model uses a two-layer LSTM network structure that supports multiple sequence feature inputs and flexible multi-step prediction outputs, which allows multi-step prediction of system states using SOFC system experimental data. Comparing the proposed model with the traditional ARIMA model and LSTM recursive prediction model, it is shown that the multi-step LSTM prediction model performs better than the ARIMA and LSTM recursive prediction models in terms of two evaluation criteria: root mean square error and mean absolute error. Thus, the proposed multi-step LSTM prediction model can effectively and accurately predict and evaluate the SOFC system’s state.