Place recognition is an important component for autonomous vehicles to achieve loop closing or global localization. In this paper, we tackle the problem of place recognition based on sequential 3D LiDAR scans obtained by an onboard LiDAR sensor. We propose a transformer-based network named SeqOT to exploit the temporal and spatial information provided by sequential range images generated from the LiDAR data. It uses multi-scale transformers to generate a global descriptor for each sequence of LiDAR range images in an end-to-end fashion. During online operation, our SeqOT finds similar places by matching such descriptors between the current query sequence and those stored in the map. We evaluate our approach on four datasets collected with different types of LiDAR sensors in different environments. The experimental results show that our method outperforms the state-of-the-art LiDAR-based place recognition methods and generalizes well across different environments. Furthermore, our method operates online faster than the frame rate of the sensor. The implementation of our method is released as open source at: https://github.com/BIT-MJY/SeqOT.