A semi-negative definite matrix gradient system representation for a type non-autonomous generalized Birkhoff system is studied. The condition under which a non-autonomous generalized Birkhoff system can be considered as semi-negative definite matrix gradient system is obtained. The characteristic of seminegative definite matrix gradient system is then used to study the stability of non-autonomous generalized Birkhoff system. Examples have been given to illustrate the applications of the results.