Recently, fog computing has been developed to complement cloud computing, which can provide cloud services at the edge of the network with real-time processing. However, the computational power of fog nodes is limited and this leads to security issues. On the other hand, cyber-attacks have become common with the exponential growth of Internet of Things (IoT) connected devices. This fact necessitates the development of Intrusion Detection Systems (IDSs) in fog environments with the aim of detecting attacks. In this paper, we develop an IDS named GAN-LSTM for fog environments that uses Generative Adversarial Networks (GANs) and Long Short-Term Memory Networks (LSTMs). GAN-LSTM is used to identify anomalies in network traffic to specific types of attacks or non-attacks. In general, GAN-LSTM consists of three components: data preprocessing, generation of real traffic patterns, and sequence analysis of real traffic data. Data preprocessing ensures data quality by removing noise and irrelevant features. The pre-processed data is fed to the GAN to generate real traffic as a baseline for normal behavior. Finally, the LSTM component is applied to detect anomalous anomalies in fog computing. The proposed algorithm was evaluated on public databases and experimental results showed that GAN-LSTM improves the accuracy of attack detection compared to equivalent approaches.