Diatoms are a type of algae with many species. Accurate and quick classification of diatom species is important in many fields, such as water quality analysis and weather change forecasting. Traditional methods for diatom classification, specifically morphological taxonomy and molecular detection, are time-consuming and may not provide satisfactory performance. However, in recent years, deep learning has demonstrated impressive performance in this task, just like other image classification problems. On the other hand, networks with more layers do not guarantee increased accuracy. While increasing depth can be useful in capturing complex features and patterns, it also introduces challenges such as vanishing gradients, overfitting, and optimization challenges. Therefore, in our work, we propose DiatomNet, a lightweight convolutional neural network (CNN) model that can classify diatom species accurately while requiring low computing resources. A recently introduced dataset consisting of 3,027 diatom images and 68 diatom species is used to train and evaluate the model. The model is compared with well-known and successful CNN models (i.e., AlexNet, GoogleNet, Inceptionv3, ResNet18, VGG16, and Xception) and their customized versions obtained with transfer learning. The comparison is based on several success metrics: accuracy, precision, recall, F-measure, number of learnable parameters, training, and prediction time. Eventually, the experimental results reveal that DiatomNet outperforms the other models regarding all metrics with just a few exceptions. Therefore, it is a lightweight but strong candidate for diatom classification tasks.