Face verification is considered to be the main part of the face detection system. To detect human faces in images, face candidates are extracted and face verification is performed. This paper proposes a new face verification algorithm using Quantum-inspired Evolutionary Algorithm (QEA). The proposed verification system is based on Principal Components Analysis (PCA). Although PCA related algorithms have shown outstanding performance, the problem lies in the selection of eigenvectors. They may not be the optimal ones for representing the face features. Moreover, a threshold value should be selected properly considering the verification rate and false alarm rate. To solve these problems, QEA is employed to find out the optimal distance measure under the predetermined threshold value which distinguishes between face images and non-face images. The proposed verification system is tested on the AR face database and the results are compared with the previous works to show the improvement in performance.