Modeling forest fire spread is a very complex problem, and the existing models usually need some input parameters which are hard to get. How to predict the time series of forest fire spread rate based on passed series may be a key problem to break through the current technical bottleneck. In the process of forest fire spreading, spread rate and wind speed would affect each other. In this paper, three kinds of network models based on Long Short-Term Memory (LSTM) are designed to predict fire spread rate, exploring the interaction between fire and wind. In order to train these LSTM-based models and validate their effectiveness of prediction, several outdoor combustion experiments are designed and carried out. Process data sets of forest fire spreading are collected with an infrared camera mounted on a UAV, and wind data sets are recorded using a anemometer simultaneously. According to the close relationship between wind and fire, three progressive LSTM based models are constructed, which are called CSG-LSTM, MDG-LSTM and FNU-LSTM, respectively. A Cross-Entropy Loss equation is employed to measure the model training quality, and then prediction accuracy is computed and analyzed by comparing with the true fire spread rate and wind speed. According to the performance of training and prediction stage, FNU-LSTM is determined as the best model for the general case. The advantage of FNU-LSTM is further demonstrated by doing comparison experiments with the normal LSTM and other LSTM based models which predict both fire spread rate and wind speed separately. The experiment has also demonstrated the ability of the model to the real fire prediction on the basis of two historical wildland fires.