Abstract: In this paper,a third-order approximation of the first-order space derivative is deduced by applying an undetermined coefficient method.Then the general approximation method for the convection flux to the derivative of the flux is extended.After introducing the TVD limiter function,we correct the third-order derivative difference approximation.Then we propose a third-order essential non-oscillatory difference scheme for solving hyperbolic conservation laws by employing the third-order Runge-Kutta method to discretize the time variable.This scheme has the advantages of simple form,less computational cost and easiness to extend the case of non-uniform grid.Finally,two standard numerical examples are given to verify the effectiveness of the scheme.