In this talk, we consider Quadratic Discriminant Analysis (QDA) and joint estimation of precision matrices for high-dimensional data. Our data-driven QDA rule incorporates precision matrices which are jointly estimated under the `Partially Common Diagonal + Low-rank' structural assumption. We provide an explicit convergence rate for the classification error of our proposed QDA rule in a similar spirit to that in Cai and Zhang (2021) but without the sparsity assumption on the difference between two precision matrices. Regarding numerical studies, we first demonstrate that the proposed QDA rule performs well, compared to other high-dimensional QDA rules, in both sparse and non-sparse cases; we then present real-data analyses based on some micro-array data sets.