Translating natural language to visualization (NL2VIS) has shown great promise for visual data analysis, but it remains a challenging task that requires multiple low-level implementations, such as natural language processing and visualization design. Recent advancements in pre-trained large language models (LLMs) are opening new avenues for generating visualizations from natural language. However, the lack of a comprehensive and reliable benchmark hinders our understanding of LLMs' capabilities in visualization generation. In this paper, we address this gap by proposing a new NL2VIS benchmark called VisEval. Firstly, we introduce a high-quality and large-scale dataset. This dataset includes 2,524 representative queries covering 146 databases, paired with accurately labeled ground truths. Secondly, we advocate for a comprehensive automated evaluation methodology covering multiple dimensions, including validity, legality, and readability. By systematically scanning for potential issues with a number of heterogeneous checkers, VisEval provides reliable and trustworthy evaluation outcomes. We run VisEval on a series of state-of-the-art LLMs. Our evaluation reveals prevalent challenges and delivers essential insights for future advancements.