Code summarization generates brief natural language descriptions of source code pieces, which can assist developers to understand code and reduce documentation workload. Recent research efforts on code summarization mainly adopt deep learning models. Most of these models are trained on large datasets, consisting of independent code-summary pairs. Despite the technical advances, most of these works, referred as general code summarization models, ignore the project-level contextual information of code pieces and summaries, which developers would heavily rely on when writing documentation. This study investigates project-specific code summarization, a scenario that is much more consistent with human behavior and tool implementation of code summarization. Specifically, a novel deep learning approach is proposed that leverages highly relevant code pieces and their corresponding summaries to characterize contextual semantics, and integrates common knowledge learned from large-scale cross-project dataset via transfer learning. The dataset is created and released for project-specific code summarization, consisting of 800k method-summary pairs along with their lifecycle information for re-producing accurate code context. Experimental results on this dataset demonstrate that the proposed technique can not only gain huge improvement over general code summarization model, but also generates more consistent summaries within a project.