Recently, unmanned aerial vehicles (UAVs) are gathering increasing attentions from both the academia and industry. The ever-growing number of UAV brings challenges for air traffic control (ATC), and thus trajectory prediction plays a vital role in ATC, especially for avoiding collisions among UAVs. However, the dynamic flight of UAV aggravates the complexity of trajectory prediction. Different with civil aviation aircrafts, the most intractable difficulty for UAV trajectory prediction depends on acquiring effective location information. Fortunately, the automatic dependent surveillance-broadcast (ADS-B) is an effective technique to help obtain positioning information. It is widely used in the civil aviation aircraft, due to its high data update frequency and low cost of corresponding ground stations construction. Hence, in this work, we consider leveraging ADS-B to help UAV trajectory prediction. However, with the ADS-B information for a UAV, it still lacks efficient mechanism to predict the UAV trajectory. It is noted that the recurrent neural network (RNN) is available for the UAV trajectory prediction, in which the long short-term memory (LSTM) is specialized in dealing with the time-series data. As above, in this work, we design a system of UAV trajectory prediction with the ADS-B information, and propose the recurrent LSTM (RLSTM) based algorithm to achieve the accurate prediction. Finally, extensive simulations are conducted by Python to evaluate the proposed algorithms, and the results show that the average trajectory prediction error is satisfied, which is in line with expectations.