Face verification is a well-known image analysis application and is widely used to recognize individuals in contemporary society. However, most real-world recognition systems ignore the importance of protecting the identity-sensitive facial images that are used for verification. To address this problem, we investigate how to implement a secure face verification system that protects the facial images from being imitated. In our work, we use the DeepID2 convolutional neural network to extract the features of a facial image and an EM algorithm to solve the facial verification problem. To maintain the privacy of facial images, we apply homomorphic encryption schemes to encrypt the facial data and compute the EM algorithm in the ciphertext domain. We develop three face verification systems for surveillance (or entrance) control of a local community based on three levels of privacy concerns. The associated timing performances are presented to demonstrate their feasibility for practical implementation.