With open-source projects growing in size and complexity, manual compilation becomes tedious and error-prone, highlighting the need for automation to improve efficiency and accuracy. However, the complexity of compilation instruction search and error resolution makes automatic compilation challenging. Inspired by the success of LLM-based agents in various fields, we propose CompileAgent, the first LLM-based agent framework dedicated to repo-level compilation. CompileAgent integrates five tools and a flow-based agent strategy, enabling interaction with software artifacts for compilation instruction search and error resolution. To measure the effectiveness of our method, we design a public repo-level benchmark CompileAgentBench, and we also design two baselines for comparison by combining two compilation-friendly schemes. The performance on this benchmark shows that our method significantly improves the compilation success rate, ranging from 10% to 71%. Meanwhile, we evaluate the performance of CompileAgent under different agent strategies and verify the effectiveness of the flow-based strategy. Additionally, we emphasize the scalability of CompileAgent, further expanding its application prospects.