It is well known that most brain disorders are complex diseases, such as Alzheimer's disease (AD) and schizophrenia (SCZ). In general, brain regions and their interactions can be modeled as complex brain network, which describe highly efficient information transmission in a brain. Therefore, complex brain network analysis plays an important role in the study of complex brain diseases. With the development of noninvasive neuroimaging and electrophysiological techniques, experimental data can be produced for constructing complex brain networks. In recent years, researchers have found that brain networks constructed by using neuroimaging data and electrophysiological data have many important topological properties, such as small-world property, modularity, and rich club. More importantly, many brain disorders have been found to be associated with the abnormal topological structures of brain networks. These findings provide not only a new perspective to explore the pathological mechanisms of brain disorders, but also guidance for early diagnosis and treatment of brain disorders. The purpose of this survey is to provide a comprehensive overview for complex brain network analysis and its applications to brain disorders.