Language model (LM) has played an increasingly important role in the common-sense understanding and reasoning in the CSQA task (Common Sense Question Answering). However, due to the amount of model parameters, increasing training data helps little in further improving model performance. Introducing external knowledge through graph neural networks (GNNs) proves positive in boosting performance, but exploiting different knowledge sources and capturing contextual information between text and knowledge inside remains a challenge. In this paper, we propose LBR-GNN, a Language-Based Reasoning Graph Neural Network method to address these problems, by representing the question with each answer and external knowledge using a language model and predicting the reasoning score with a designed language-based GNN. Our LBR-GNN will first regulate external knowledge into a consistent textual form and encode it using a standard LM to capture the contextual information. Then, we build a graph neural network using the encoded information, especially the language-level edge representation. Finally, we design a novel edge aggregation method to select the edge information for GNN update and the language-guided GNN reasoning. We assess the performance of LBR-GNN across the CommonsenseQA, CommonsenseQA-IH, and OpenBookQA datasets. Our evaluation reveals a performance boost of more than 5% compared to the state-of-the-art methods on the CSQA dataset, achieved with a similar number of additional parameters.