Automatic code summarization is an important topic in the software engineering field, which aims to automatically generate the description for the source code. Based on Graph Neural Networks (GNN), most existing methods apply them to Abstract Syntax Tree (AST) to achieve code summarization. However, these methods face two major challenges: 1) they can only capture limited structural information of the source code; 2) they did not effectively solve Out-Of-Vocabulary (OOV) problems by reducing vocabulary size. In order to resolve these problems, in this paper, we propose a novel code summarization model named Dynamic Graph attention-based Transformer (DG-Trans for short), which effectively captures abundant information of the code subword sequence and utilizes the fusion of dynamic graph attention mechanism and Transformer. Extensive experiments show that DG-Trans is able to outperform state-of-the-art models (such as Ast-Attendgru, Transformer, and CodeGNN) by averagely increasing 8.39% and 8.86% on BLEU scores and ROUGUE-L, respectively.