Face Recognition is one of the prominent problems in the computer vision domain. Witnessing advances in deep learning, significant work has been observed in face recognition, which touched upon various parts of the recognition framework like Convolutional Neural Network (CNN), Layers, Loss functions, etc. Various loss functions such as Cross-Entropy, Angular-Softmax and ArcFace have been introduced to learn the weights of network for face recognition. However, these loss functions are not able to priorities the hard samples as compared to easy samples. Moreover, their learning process is biased due to a number of easy examples compared to hard examples. In this paper, we address this issue by considering hard examples with more priority. In order to do so, We propose a Hard-Mining loss by by increasing the loss for harder examples and decreasing the loss for easy examples. The proposed concept is generic and can be used with any existing loss function. We test the Hard-Mining loss with different losses such as Cross-Entropy, Angular-Softmax and ArcFace. The proposed Hard-Mining loss is tested over widely used the Labeled Faces in the Wild (LFW) and YouTube Faces (YTF) datasets while training is performed over CASIA-WebFace and MS-Celeb-1M datasets. We use the residual network (i.e., ResNet18) for the experimental analysis. The experimental results suggest that the performance of existing loss functions is boosted when used in the framework of the proposed Hard-Mining loss.