Performance anomalies represent the performance degradation issues (e.g., slowing down in system response times) of software systems at run-time. Prior studies propose different approaches to detect anomalies by analyzing execution logs and resource utilization metrics after the anomalies have happened. However, the prior detection approaches cannot predict the anomalies ahead of time; such limitation causes an inevitable delay in taking corrective actions to prevent performance anomalies from happening. We propose an approach that can \textit{predict performance anomalies} in software systems and raise anomaly warnings in advance. Our approach uses a Long-Short Term Memory (LSTM) neural network to capture the normal behaviors of a software system. Then, our approach predicts performance anomalies by identifying the early deviations from the captured normal system behaviors. We conduct extensive experiments to evaluate our approach using two real-world software systems (i.e., Elasticsearch and Hadoop).