Stability of cellular neural networks is significant because it has been used in a certain application areas as im}r ge processing, video communication, optimal control and so on. How to choose a reasonable template of the parameters is the key issue of stability researches. Lyapunov second method was used to analyze the global asymptotic stability of cellular neural networks, and a better I_yapunov function was constructed to receive a new sufficient condition for deter- mining the global asymptotic stability of the system. The condition improves previous results and further derives a suffi- cicnt condition when original point is equilibrium point. Numerical simulations show their effectiveness and feasibility.