In face recognition, distinguishing identical twins faces is a challenging task because of the high level of correlation in facial appearance.Generally, facial recognition is easy to make mistakes when it comes to twins or similar faces. To deal with the high level of correlation in similar faces, we proposed a deep convolutional neural network (CNN) using triplet loss function to differentiate the identical twins. We applied a hybrid strategy by combining the deep CNN model, which learns an embedding from facial images to Euclidean space and triplet loss function to evaluate the L2 distance between facial images into Euclidean space, Obtained L2 distance shows the level of similarity between corresponding faces. We implemented two different CNN models on our raw pixel images; additionally, we used different techniques to reduce the overfitting problem such as dropout and batch normalization, additionally L2 regularization. Our method achieves the best mean validation accuracy above 87.2%.