Code summarization generates brief natural language descriptions of source code pieces, which can assist developers in understanding code and reduce documentation workload. Recent neural models on code summarization are trained and evaluated on large-scale multi-project datasets consisting of independent code-summary pairs. Despite the technical advances, their effectiveness on a specific project is rarely explored. In practical scenarios, however, developers are more concerned with generating high-quality summaries for their working projects. And these projects are usually poorly documented, hence having few historical code-summary pairs. To this end, we investigate low-resource project-specific code summarization, a novel task more consistent with the developers’ requirements. To better characterize project-specific knowledge with limited training samples, we propose a meta transfer learning method by incorporating a lightweight fine-tuning mechanism into a meta-learning framework. Experimental results on nine real-world projects verify the superiority of our method over alternative ones and reveal how the project-specific knowledge is learned.