Nowadays, hackers take illegal advantage of distributed resources in a network of computing devices (i.e., botnet) to launch cyberattacks against the Internet of Things (IoT). Recently, diverse Machine Learning (ML) and Deep Learning (DL) methods were proposed to detect botnet attacks in IoT networks. However, highly imbalanced network traffic data in the training set often degrade the classification performance of state-of-the-art ML and DL models, especially in classes with relatively few samples. In this paper, we propose an efficient DL-based botnet attack detection algorithm that can handle highly imbalanced network traffic data. Specifically, Synthetic Minority Oversampling Technique (SMOTE) generates additional minority samples to achieve class balance, while Deep Recurrent Neural Network (DRNN) learns hierarchical feature representations from the balanced network traffic data to perform discriminative classification. We develop DRNN and SMOTE-DRNN models with the Bot-IoT dataset, and the simulation results show that high-class imbalance in the training data adversely affects the precision, recall, F1 score, area under the receiver operating characteristic curve (AUC), geometric mean (GM) and Matthews correlation coefficient (MCC) of the DRNN model. On the other hand, the SMOTE-DRNN model achieved better classification performance with 99.50% precision, 99.75% recall, 99.62% F1 score, 99.87% AUC, 99.74% GM and 99.62% MCC. Additionally, the SMOTE-DRNN model outperformed state-of-the-art ML and DL models.