Text classification plays an important role in various downstream text-related tasks, such as sentiment analysis, fake news detection, and public opinion analysis. Recently, text classification based on Graph Neural Networks (GNNs) has made significant progress due to their strong capabilities of structural relationship learning. However, these approaches still face two major limitations. First, these approaches fail to fully consider the diverse structural information across word pairs, e.g., co-occurrence, syntax, and semantics. Furthermore, they neglect sequence information in the text graph structure information learning module and can not classify texts with new words and relations. In this paper, we propose a Novel Graph-Sequence Learning Model for Inductive Text Classification (TextGSL) to address the previously mentioned issues. More specifically, we construct a single text-level graph for all words in each text and establish different edge types based on the diverse relationships between word pairs. Building upon this, we design an adaptive multi-edge message-passing paradigm to aggregate diverse structural information between word pairs. Additionally, sequential information among text data can be captured by the proposed TextGSL through the incorporation of Transformer layers. Therefore, TextGSL can learn more discriminative text representations. TextGSL has been comprehensively compared with several strong baselines. The experimental results on diverse benchmarking datasets demonstrate that TextGSL outperforms these baselines in terms of accuracy.