Fish is an important part of Bangladeshi culture and cuisine. Fish is the main and sometimes the only source of protein in the rural household of Bangladesh. Moreover, thousands of peoples of Bangladesh are directly and indirectly dependent on the fish industry. With time many traditional indigenous Bangladeshi fish has lost their existence and many of them are in danger of losing their existence. Furthermore, the young generation of Bangladesh is unable to recognize these traditional indigenous fishes besides they are also missing out on the protein and nutrition provided by these indigenous fishes. Hence an automatic fish classification system can help us not only to recognize traditional fishes but also in the production and preservation of these indigenous fishes. So, in this paper, we propose a convolutional neural network (CNN) based automatic fish classification system. In this paper, we mainly focus on the classification of traditional indigenous fishes of Bangladesh. We used a dataset of eight classes of indigenous fish which contains 8000 images after performing 8 types of augmentation methods. We fed our data to VGG16, Inception V3, MobileNet pre-train models with slight modification in the output layer. We also applied this dataset to a 5 layers CNN model which we name FishNet, where convolutional layers of the CNN model uses "Adam optimizer", "ReLU" and the "SoftMax" activation function. FishNet surpasses VGG16 in all the performance measures and goes toe to toe with InceptionV3 and MobileNet models. Finally, we see all the models provide excellent performance measures.