A generalized system-optimal（SO）traffic assignment model with link capacity constraints and and general polynomial link impedance functions was proposed to define optimal traffic assignment. The study extended the traditional convex SO model to general cases. The nonconvexity of many general system-optimal traffic assignment problems makes it difficult to obatin the global optimum through traditional optimization methods. To this end, this paper proposed the Moment Semidefinite Programming (MSDP) relaxation technique which can get the global optimum for general system optimal traffic assignment problems. Two numerical examples were used to illustrate the proposed model and solution method. Numerical results show that the MSDP method can solve the classical convex SO traffic assignment problem directly, and can also deal with the general system optimal traffic assignment with link capacity constraints and general polynomial link impedance functions.