Short text classification is an important problem of natural language processing (NLP), and graph neural networks (GNNs) have been successfully used to solve different NLP problems. However, few studies employ GNN for short text classification, and most of the existing graph-based models ignore sequential information (e.g., word orders) in each document. In this work, we propose an improved sequence-based feature propagation scheme, which fully uses word representation and document-level word interaction and overcomes the limitations of textual features in short texts. On this basis, we utilize this propagation scheme to construct a lightweight model, sequential GNN (SGNN), and its extended model, ESGNN. Specifically, we build individual graphs for each document in the short text corpus based on word co-occurrence and use a bidirectional long short-term memory network (Bi-LSTM) to extract the sequential features of each document; therefore, word nodes in the document graph retain contextual information. Furthermore, two different simplified graph convolutional networks (GCNs) are used to learn word representations based on their local structures. Finally, word nodes combined with sequential information and local information are incorporated as the document representation. Extensive experiments on seven benchmark datasets demonstrate the effectiveness of our method.