A Distributed Denial-of-service (DDoS) attack is a malicious attempt to disrupt the regular traffic of a targeted server, service, or network by sending a flood of traffic to overwhelm the target or its surrounding infrastructure. As technology improves, new attacks have been developed by hackers. Traditional statistical and shallow machine learning techniques can detect superficial anomalies based on shallow data and feature selection, however, these approaches cannot detect unseen DDoS attacks. In this context, we propose a reconstruction-based anomaly detection model named LSTM-Autoencoder (LSTM-AE) which combines two deep learning-based models for detecting DDoS attack anomalies. The proposed structure of long short-term memory (LSTM) networks provides units that work with each other to learn the long short-term correlation of data within a time series sequence. Autoencoders are used to identify the optimal threshold based on the reconstruction error rates evaluated on each sample across all time-series sequences. As such, a combination model LSTM-AE can not only learn delicate sub-pattern differences in attacks and benign traffic flows, but also minimize reconstructed benign traffic to obtain a lower range reconstruction error, with attacks presenting a larger reconstruction error. In this research, we trained and evaluated our proposed LSTM-AE model on reflection-based DDoS attacks (DNS, LDAP, and SNMP). The results of our experiments demonstrate that our method performs better than other state-of-the-art methods, especially for LDAP attacks, with an accuracy of over 99.