A new Lyapunov functional is used to analyze the asymptotic stability of sampled-data systems under aperiodic sampling.A Lyapunov functional is constructed by introducing the integral of the state and the cross term of this integral and the sampling state.The improved Jensen inequality reported recently is used to estimate the derivative of the Lyapunov functional.A new asymptotic stability result is obtained for the sampled-data systems under aperiodic sampling.The simulation results show that the proposed result has less conservatism than some existing ones.