In this paper, we mainly intend to address the underwater image classification problem in an open-set scenario. Image classification algorithms have been mostly provided with a small set of species, while there exist lots of species not available to the algorithms or even unknown to ourselves. Thus, we deal with an open-set problem and extremely high false alarm rate in real scenarios, especially in the case of unseen species. Motivated by these challenges, our proposed scheme aims to prevent the unseen species from going to the classifier section. To this end, we introduce a new framework based on convolutional neural networks (CNNs) that automatically identifies various species of fishes and then classifies them into certain classes using a novel technique. In the proposed method, an autoencoder is employed to distinguish between seen and unseen species. To clarify, the autoencoder is trained to reconstruct the available species with high accuracy and filter out species that are not in our training set. In the following, a classifier based on EfficientNet is trained to classify the samples that are accepted by the autoencoder (AE), i.e. the samples that have small reconstruction error. Our proposed method is evaluated in terms of precision, recall, and accuracy and compared to the state-of-the-art methods utilizing WildFish dataset. Simulation results reveal the supremacy of the proposed method.