In this paper, we present an auto-tuning method for Linear Quadratic Regulator (LQR) based on correlation analysis. Unlike previous studies which focused on LQR tuning strategies exclusively by evaluating the control performance, we propose to explore the explicit relationship between the model and weighting parameters in LQR. The objective of this paper is twofold: (1) we introduce an approach to the identification and quantification of the correlation between a model parameter and a weighting parameter in LQR; (2) an auto-tuning method is worked out which is explicitly related to the variation of the model parameter. As a result, an optimal value of the weighting parameter can be effectively determined and, in the meantime, the parameter variation estimated. Through the numerical example, we demonstrate the effectiveness of the proposed auto-tuning method in restoring the control performance under unknown parameter variations.