This paper proposes an efficient design optimization algorithm for the multidisciplinary design optimization of link mechanisms. Since the design problem of link mechanisms is multidisciplinary and mini-max type under time-dependence of link motion, the algorithm is composed of non-hierarchic coupled system decomposition, which consists of the iteration of partial optimization of divided subproblems and coordination of such partial solutions, and mini-max relaxation. Further, successive quadratic programming (SQP) is used as a mathematical programming technique by inheriting Hessian approximation of Lagrangian function across its iterative executions. After the multidisciplinary design problem of a link mechanism used in hydraulic shovels is formulated, its design optimization with the proposed method is demonstrated. The numerical results show more than about four times of speed-up and robust performance as compared with a conventional optimization method.