The emergence of biometric tools and its increased usage in day to day devices has brought simplicity in the authentication process for the users as compared to the passwords and pattern locks being used. The ease of use of biometric reduces the manual work and helps in faster and automatic authentication. Among different biometric traits, the face is one which can be captured without much cooperation of users. Moreover, face recognition is one of the most widely publicized feature in the devices today and hence represents an important problem that should be studied with the utmost priority. As per the recent trends, the Convolutional Neural Network (CNN) based approaches are highly successful in many tasks of Computer Vision including face recognition. The loss function is used on the top of CNN to judge the goodness of any network. The loss functions play an important role in CNN training. Basically, it generates a huge loss, if the network does not perform well using the current parameter setting. In this paper, we present a performance comparison of different loss functions such as Cross-Entropy, Angular Softmax, Additive-Margin Softmax, ArcFace and Marginal Loss for face recognition. The experiments are conducted with two CNN architectures namely, ResNet and MobileNet. Two widely used face datasets namely, CASIA-Webface and MS-Celeb-1M are used for the training and benchmark Labeled Faces in the Wild (LFW) face dataset is used for the testing. The training and test results are analyzed in this paper.