Networking Function Virtualization (NFV) technology has become a new solution for running network applications. It proposes a new paradigm for network function management and has brought much innovation space for the network technology. However, the complexity of the NFV Infrastructure (NFVI) impose hard-to-predict relationship between Virtualized Network Function (VNF) performance metrics (e.g., latency, throughput), the underlying allocated resources (e.g., load of vCPU), and the overall system workload, thus the evolving scenario of NFV calls for adequate performance analysis methodologies, early detection of performance anomalies plays a significant role in providing high-quality network services. In this paper, we have proposed a novel method for detecting the performance anomalies in NFV infrastructure with machine learning methods. We present a case study on the open source NFV-oriented project, namely Clearwater, which is an IP Multimedia Subsystem (IMS) NFV application. Several classical classifiers are applied and compared empirically on the anomaly dataset which is built by ourselves. Considering the risk of over-fitting issue, the experimental results show that neutral networks is the best anomaly detection model with the accuracy over 94%.