Project-specific code completion is a critical task that leverages context from a project to generate accurate code. State-of-the-art methods use retrieval-augmented generation (RAG) with large language models (LLMs) and project information for code completion. However, they often struggle to incorporate internal API information, which is crucial for accuracy, especially when APIs are not explicitly imported in the file. To address this, we propose a method to infer internal API information without relying on imports. Our method extends the representation of APIs by constructing usage examples and semantic descriptions, building a knowledge base for LLMs to generate relevant completions. We also introduce ProjBench, a benchmark that avoids leaked imports and consists of large-scale real-world projects. Experiments on ProjBench and CrossCodeEval show that our approach significantly outperforms existing methods, improving code exact match by 22.72% and identifier exact match by 18.31%. Additionally, integrating our method with existing baselines boosts code match by 47.80% and identifier match by 35.55%.