Counterfactual explanations promote explainability in machine learning models by answering the question “how should the input instance be altered to obtain a desired predicted label?". The comparison of this instance before and after perturbation can enhance human interpretation. Most existing studies on counterfactual explanations are limited in tabular data or image data. In this paper, we study the problem of counterfactual explanation generation on graphs. A few studies have explored to generate counterfactual explanations on graphs, but many challenges of this problem are still not well-addressed: 1) optimizing in the discrete and disorganized space of graphs; 2) generalizing on unseen graphs; 3) maintaining the causality in the generated counterfactuals without prior knowledge of the causal model. To tackle these challenges, we propose a novel framework CLEAR which aims to generate counterfactual explanations on graphs for graph-level prediction models. Specifically, CLEAR leverages a graph variational autoencoder based mechanism to facilitate its optimization and generalization, and promotes causality by leveraging an auxiliary variable to better identify the causal model. Extensive experiments on both synthetic and real-world graphs validate the superiority of CLEAR over state-of-the-art counterfactual explanation methods on graphs in different aspects.