Objective. The prevalence of acrophobia is high, especially with the rise of many high-rise buildings. In the recent few years, researchers have begun to analyze acrophobia from the neuroscience perspective, especially to improve the virtual reality exposure therapy (VRET). Electroencephalographic (EEG) is an informative neuroimaging technique, but it is rarely used for acrophobia. The purpose of this study is to evaluate the effectiveness of using EEGs to identify the degree of acrophobia objectively. Approach. EEG data were collected by virtual reality (VR) exposure experiments. We classified all subjects’ degrees of acrophobia into three categories, where their questionnaire scores and behavior data showed significant differences. Using synchronization likelihood, we computed the functional connectivity between each pair of channels and then obtained complex networks named functional brain networks (FBNs). Basic topological features and community structure features were extracted from the FBNs. Statistical results demonstrated that FBN features can be used to distinguish different groups of subjects. We trained machine learning (ML) algorithms with FBN features as inputs and trained convolutional neural networks (CNNs) with FBNs directly as inputs. Main results. It turns out that using FBN to identify the severity of acrophobia is feasible. For ML algorithms, the community structure features of some cerebral cortex regions outperform typical topological features of the whole brain, in terms of classification accuracy. The performances of CNN algorithms are better than ML algorithms. The CNN with ResNet performs the best (accuracy reached 98.46 ± 0.42%). Significance. These observations indicate that community structures of certain cerebral cortex regions could be used to identify the degree of acrophobia. The proposed CNN framework can provide objective feedback, which could help build closed-loop VRET portable systems.