In current research on automatic essay scoring, related work tends to focus more on evaluating the overall quality or a single trait of prompt-specific essays. However, when scoring essays in an educational context, it is essential not only to consider the overall score but also to provide feedback on various aspects of the writing. This helps students clearly identify areas for improvement, enabling them to engage in targeted practice. Although many methods have been proposed to address the scoring issue, they still suffer from insufficient learning of trait representations and overlook the diversity and correlations between trait scores in the scoring process. To address this problem, we propose a novel multi-trait essay scoring method based on Trait-Aware Mix-of-Experts Representation Learning. Our method obtains trait-specific essay representations using a Mix-of-Experts scoring architecture. Furthermore, based on this scoring architecture, we propose a diversified trait-expert method to learn distinguishable expert weights. And to facilitate multi-trait scoring, we introduce two trait correlation learning strategies that achieve learning the correlations among traits. Experimental results demonstrate the effectiveness of our method, and compared to existing methods, it achieves a further improvement in computational efficiency.