Software size estimation is a crucial step in project management. According to the Standish Chaos Report, 65% of software projects are over budget or deadline; therefore, a good size estimation method is very important. However, existing estimation methods are complicated and human-effort consuming. In many industrial projects, project technical leads (PTLs) do not use these methods but just give a rough estimation based on their experience. To decrease human effort, we propose an early software size estimation (ESSE) method, which can extract semantic features from natural language requirements automatically, and build size estimation models for project. Firstly, ESSE makes a two-level semantic analysis of requirements specification documents by information extraction and activation spreading. Then, complexity-related features are extracted from the results of semantic analysis. Finally, a size estimation model is trained to predict size of new projects by regression algorithms. Experiments in real industrial datasets show that our method is effective and can be applied to real industrial projects.