Sign language production aims to automatically generate coordinated sign language videos from spoken language. As a typical sequence to sequence task, the existing methods are mostly to regard the skeletons as a whole sequence, however, those do not take the rich graph information among both joints and edges into consideration. In this paper, we propose a novel method named Spatial-Temporal Graph Transformer (STGT) to deal with this problem. Specifically, according to kinesiology, we first design a novel graph representation to achieve graph features from skeletons. Then the spatial-temporal graph selfattention utilizes graph topology to capture the intra-frame and inter-frame correlations, respectively. Our key innovation is that the attention maps are calculated on both spatial and temporal dimensions in turn, meanwhile, graph convolution is used to strengthen the short-term features of skeletal structure. Finally, due to the generated skeletons are based on the form of skeleton points and lines so far. In order to visualize the generated sign language videos, we design a sign mesh regression module to render the skeletons into skinned animations including body and hands posture. Comparing with states of art baseline on RWTH-PHONEIX Weather-2014T in Experiment Section, STGT can obtain the highest values on BLEU and ROUGE, which indicates our method produces most accurate and intuitive sign language videos.