As a promising candidate to complement traditional biometric modalities, brain biometrics using electroencephalography (EEG) data has received a widespread attention in recent years. However, compared with existing biometrics such as fingerprints and face recognition, research on EEG biometrics is still in its infant stage. Most of the studies focus on either designing signal elicitation protocols from the perspective of neuroscience or developing feature extraction and classification algorithms from the viewpoint of machine learning. These studies have laid the ground for the feasibility of using EEG as a biometric authentication modality, but they have also raised security and privacy concerns as EEG data contains sensitive information. Existing research has used hash functions and cryptographic schemes to protect EEG data, but they do not provide functions for revoking compromised templates as in cancellable template design. This paper proposes the first cancellable EEG template design for privacy-preserving EEG-based authentication systems, which can protect raw EEG signals containing sensitive privacy information (e.g., identity, health and cognitive status). A novel cancellable EEG template is developed based on EEG graph features and a non-invertible transform. The proposed transformation provides cancellable templates, while taking advantage of EEG elicitation protocol fusion to enhance biometric performance. The proposed authentication system offers equivalent authentication performance (8.58\% EER on a public database) as in the non-transformed domain, while protecting raw EEG data. Furthermore, we analyze the system's capacity for resisting multiple attacks, and discuss some overlooked but critical issues and possible pitfalls involving hill-climbing attacks, second attacks, and classification-based authentication systems.