We present a long short-term memory (LSTM) network for predicting whether an active region (AR) would produce a -class flare within the next 24 hr. We consider three classes, namely ≥M5.0 class, ≥M class, and ≥C class, and build three LSTM models separately, each corresponding to a class. Each LSTM model is used to make predictions of its corresponding -class flares. The essence of our approach is to model data samples in an AR as time series and use LSTMs to capture temporal information of the data samples. Each data sample has 40 features including 25 magnetic parameters obtained from the Space-weather HMI Active Region Patches and related data products as well as 15 flare history parameters. We survey the flare events that occurred from 2010 May to 2018 May, using the Geostationary Operational Environmental Satellite X-ray flare catalogs provided by the National Centers for Environmental Information (NCEI), and select flares with identified ARs in the NCEI flare catalogs. These flare events are used to build the labels (positive versus negative) of the data samples. Experimental results show that (i) using only 14-22 most important features including both flare history and magnetic parameters can achieve better performance than using all 40 features together; (ii) our LSTM network outperforms related machine-learning methods in predicting the labels of the data samples. To our knowledge, this is the first time that LSTMs have been used for solar-flare prediction.