Abstract: The new-type entropy stable schemes were proposed for the hyperbolic conservation systems. The Central Weighted Essentially Non-Oscillatory (CWENO) reconstruction was used in space and the strong stability-preserving Runge-Kutta (Runge-Kutta) method of fourth-order was utilized in time for the new algorithm. Some numerical examples of one-dimensional Burgers equation and Euler systems were solved by the new scheme. According to the results, the new method has higher-accuracy and can effectively inhibit spurious oscillations, which identifies with the theoretical analysis.