Despite the huge success of deep convolutional neural networks in face recognition (FR) tasks, current methods lack explainability for their predictions because of their ``black-box'' nature. In recent years, studies have been carried out to give an interpretation of the decision of a deep FR system. However, the affinity between the input facial image and the extracted deep features has not been explored. This paper contributes to the problem of explainable face recognition by first conceiving a face reconstruction-based explanation module, which reveals the correspondence between the deep feature and the facial regions. To further interpret the decision of an FR model, a novel visual saliency explanation algorithm has been proposed. It provides insightful explanation by producing visual saliency maps that represent similar and dissimilar regions between input faces. A detailed analysis has been presented for the generated visual explanation to show the effectiveness of the proposed method.