With the development of internet technology, more and more risks are appearing on the internet and the internet security has become an important issue. Intrusion detection technology is an important part of internet security. In intrusion detection, it is important to have a fast and effective method to find out known and unknown attacks. In this paper, we present a graph-based intrusion detection algorithm by outlier detection method which is based on local deviation factor (LDFGB). This algorithm has better detection rates than a previous clustering algorithm. Moreover, it is able to detect any shape of cluster and still keep high detection rate for detecting unknown or known attacks. LDFGB algorithm uses graph-based cluster algorithm (GB) to get an initial partition of dataset which depends on a parameter of cluster precision, then we use the outlier detection algorithm to further processing the results of graph-based cluster algorithm. This measure is effective to improve the detection rates and false positive rates.