<p>Quasi-Newton methods are considered as the effective approaches for solving multiobjective optimization problems and have emerged as a prominent research area in this field. However, to the best of our knowledge, there is currently no existing diagonal quasi-Newton method specifically designed for addressing multiobjective optimization problems. In this paper, we propose a modified diagonal BFGS method tailored for tackling such problems. The proposed approach utilizes a common diagonal positive definite matrix to approximate the Hessian matrices of objective functions. This diagonal matrix corresponds to the diagonal component of the modified BFGS update matrix. By incorporating Wolfe line search, our proposed method demonstrates the global convergence properties even without assuming convexity on the objective functions. Furthermore, we establish R-linear convergence towards Pareto optimal points for strongly convex multiobjective problems. Numerical experiments validate the practical efficiency of our proposed diagonal quasi-Newton method.</p>