A brain-computer interface (BCI) enables direct communication between the brain and an external device. Electroencephalogram (EEG) is the preferred input signal in non-invasive BCIs, due to its convenience and low cost. EEG-based BCIs have been successfully used in many applications, such as neurological rehabilitation, text input, games, and so on. However, EEG signals inherently carry rich personal information, necessitating privacy protection. This paper demonstrates that multiple types of private information (user identity, gender, and BCI-experience) can be easily inferred from EEG data, imposing a serious privacy threat to BCIs. To address this issue, we design perturbations to convert the original EEG data into privacy-protected EEG data, which conceal the private information while maintaining the primary BCI task performance. Experimental results demonstrated that the privacy-protected EEG data can significantly reduce the classification accuracy of user identity, gender and BCI-experience, but almost do not affect at all the classification accuracy of the primary BCI task, enabling user privacy protection in EEG-based BCIs.