Long-running software system tends to show performance degradation and sudden failures, due to error accumulation or resource exhaustion over time. This phenomenon is usually called software aging. Software aging is an important factor that influences software reliability. This paper presents a prediction method to investigate software aging in an OpenStack cloud system. At first, the performance data in an OpenStack cloud system is monitored and collected. Then, an autoregressive integrated moving averages (ARIMA) approach is used to predict the performance data. Finally, the experimental results and statistical analysis of collected data validate the presence of software aging in the OpenStack cloud system.