This paper proposes a novel stability criterion for non-autonomous generalized Birkhoff systems based on triple combined gradient system framework. Firstly, the differential equations and fundamental properties of four distinct gradient systems and their corresponding triple combined gradient systems are systematically discussed. Secondly, for the governing differential equations of non-autonomous generalized Birkhoff systems, a representation method based on matrix combinations is proposed, establishing four different forms of triple combined gradient representations. On this basis, the Lyapunov function can be directly derived from the corresponding triple combined gradient representation equations via given matrix combinations, thereby simplifying the stability determination process. Compared with existing methods, the proposed approach significantly reduces the difficulty associated with constructing Lyapunov functions, providing an effective tool for studying the stability of non-autonomous generalized Birkhoff systems. Finally, the validity and accuracy of the proposed method are verified through stability analysis and numerical simulations of representative examples.