Emotion analysis can quickly and accurately dig out users’ emotional tendencies， and has a huge application market. Aiming at the complexity and diversity of the microblog language’s syntactic structures， a Syntax Graph Convolution Network （SGCN） model was proposed for fine-grained emotion classification of Chinese microblog. The proposed model has the characteristics of rich structural and semantic expression at the same time. In the model， a text graph was constructed on the basis of the dependency between words， and the correlation degree between words was quantified by Pointwise Mutual Information （PMI）. After that， the PMI was used as the weight of the corresponding edge to represent the structural information of the sentence. The semantic features fusing location information were taken as the initial features of nodes to increase the semantic features of nodes in the text graph. Experimental results on the microblog emotion classification dataset of Social Media Processing 2020 （SMP2020） show that for two sets of microblog data containing six categories of emotions： happiness， sadness， anger， fear， surprise， and emotionlessness， the average F1-score of the proposed model reaches 72.64% which is 2.75 and 3.87 percentage points higher than those of the BERT （Bidirectional Encoder Representations from Transformers） Graph Convolutional Network （BGCN） model and the Text Level Graph Neural Network （Text-Level-GNN） model， verifying that the proposed model can use the structural information of sentences more effectively to improve the classification performance than other deep learning models.