This paper studies the problem of asymptotic stability for a class of nonlinear systems with state time-delay by using sampled-data control method. The key technology to solve this problem is the dispose of time-delay, as well as the error estimate of state growth which is resulted by using sampled-data methods. Since the time delay is a constant, it can be divided into several intervals which have the same length as the sampling period. Based on this division, a mathematical induction approach is proposed to estimate the state growth. A scaling gain is introduced by coordinate transformation to deal with the nonlinear terms of the system, and then the state observer and controller are designed, which contain the scaling gain via the sampled-data control method. Combined with the Lyapunov functional method of nonlinear time-delay systems, the stability of the closed-loop system is analyzed, and finally the appropriate scaling gain and sampling period are determined to guarantee the asymptotic stability of the closed-loop system. The numerical example verifies the availability of the method and the obtained results.