Code vulnerability detection (CVD) is essential for addressing and preventing system security issues, playing a crucial role in ensuring software security. Previous learning-based vulnerability detection methods rely on either fine-tuning medium-size sequence models or training smaller neural networks from scratch. Recent advancements in large pre-trained language models (LLMs) have showcased remarkable capabilities in various code intelligence tasks including code understanding and generation. However, the effectiveness of LLMs in detecting code vulnerabilities is largely under-explored. This work aims to investigate the gap by fine-tuning LLMs for the CVD task, involving four widely-used open-source LLMs. We also implement other five previous graph-based or medium-size sequence models for comparison. Experiments are conducted on five commonly-used CVD datasets, including both the part of short samples and long samples. In addition, we conduct quantitative experiments to investigate the class imbalance issue and the model's performance on samples of different lengths, which are rarely studied in previous works. To better facilitate communities, we open-source all codes and resources of this study in https://github.com/SakiRinn/LLM4CVD and https://huggingface.co/datasets/xuefen/VulResource.