Prognostics and health management (PHM) are gradually being applied to production management processes as industrial production is gradually undergoing a transformation, turning into intelligent production and leading to increased demands on the reliability of industrial equipment. Remaining useful life (RUL) prediction plays a pivotal role in this process. Accurate prediction results can effectively provide information about the condition of the equipment on which intelligent maintenance can be based, with many methods applied to this task. However, the current problems of inadequate feature extraction and poor correlation between prediction results and data still affect the prediction accuracy. To overcome these obstacles, we constructed a new fusion model that extracts data features based on a broad learning system (BLS) and embeds long short-term memory (LSTM) to process time-series information, named as the B-LSTM. First, the LSTM controls the transmission of information from the data to the gate mechanism, and the retained information generates the mapped features and forms the feature nodes. Then, the random feature nodes are supplemented by an activation function that generates enhancement nodes with greater expressive power, increasing the nonlinear factor in the network, and eventually the feature nodes and enhancement nodes are jointly connected to the output layer. The B-LSTM was experimentally used with the C-MAPSS dataset and the results of comparison with several mainstream methods showed that the new model achieved significant improvements.