Abstract: Due to the nonsmooth property of eigenvalue function, existing algorithms could not solve the coordination problem of power system stabilizer (PSS) with optimality and convergence guarantees. To tackle the problem, this paper proposed a sequential quadratic programming (SQP) method to simultaneously coordinate and optimize the parameters of PSS by using a gradient sampling (GS) theory, which was the latest advance of the nonsmooth optimization. The method deduced the formulation for gradients of the eigenvalue with respect to PSS parameters. The gradients were evaluated at the iteration point and randomly generated points in its neighborhood, forming the convex hull to approximate the subgradient of spectral abscissa with respect to PSS parameters in the iteration. A quadratic programming (QP) problem that minimizing the projection from the origin to the subgradient was formulated and solved to obtain a search direction. The sequential quadratic programming method with gradient sampling (SQP-GS) could theoretically guarantee global convergence, and the optimal goal of parameter coordination was achieved. Tests on the WSCC 3-machine 9-bus system, New England 10-machine 39-bus system, and IEEE 54-machine 118-bus system show that the damping effect and the computing efficiency of SQP-GS are better than that of heuristic algorithms.