Studies have shown that peer evaluation is effective in improving learner feedback literacy and quality. However, evaluators have few opportunities to express their views in traditional peer evaluation. This study introduced backwards feedback based on traditional peer evaluation and constructed a dual-cycle peer evaluation model to enhance learner feedback literacy and quality. We analysed learners' feedback literacy and quality before and after the application of the model, and explored the correlations between the two abilities over time. A total of 24 undergraduate students participated in the experiment using the dual-cycle peer evaluation tool. Changes in learners' feedback literacy and quality were examined using Epistemic Network Analysis and Latent Transition Analysis. The dual-cycle peer evaluation model was effective in enhancing learners' feedback literacy, increasing the depth of feedback content, and facilitating learners' integration in multiple and multidimensional evaluations. High feedback literacy positively affected students' evaluation performance, and those with high literacy demonstrated more higher-order cognitive abilities and more diversified evaluations. The findings may be instructive for teachers or learning platform developers designing mechanisms for peer evaluation.