In this paper, we concentrate on the non-convex optimization (nc-PL) problem under Polyak-Šojasiewicz condition. Most existing non-convex optimization algorithms for nc-PL utilize the dynamical systems to observe the iterative behavior trajectories. However, the dynamical systems often yield oscillations due to its undamped form, which leads to slow convergence or divergence. To solve this problem, we derive a second-order continuous dynamical system with Hessian-driven damping, which can avoid oscillations. By Cauchy-Lipschitz-Picard theorem, we first derive the existence and uniqueness of global solution for this dynamical system. Further, we present the stability of small perturbation around the global solution and the asymptotic convergence of the objective function along the trajectories generated by the dynamical system for solving nc-PL without assuming uniqueness of the minimizer. Moreover, we show the linear convergence rate of the dynamical system for smooth convex optimization. Finally, by replacing the objective function f by its Moreau envelope, we extend the results to the case of non-smooth convex functions.