The propagation mode of the elastic wave in phononic crystals is determined by its dispersion relation. Starting from the wave equation of two-dimensional infinite periodic structure and introducing the Bloch theory and small parametric perturbation expansion method， a first-order approximate perturbation method for analyzing the dispersion relationship of nonlinear discrete phononic crystals is proposed. And the first-order dispersion relations and dispersion curves are obtained to analyze the effects of impedance configuration and nonlinear coefficient pair frequency on dispersion and group velocity in different directions. Two-dimensional single-atom lattices， two-dimensional two-atom two-degree-of-freedom grids， and two-dimensional two-atom four-degree-of-freedom grids are used as examples. Their first-order dispersion curves are obtained. Dispersion results are displayed. Dispersion results reveal that band gap and direction of propagation are related to theamplitude of the wave. Finally，combining with the numerical integral result to verify the solution’s accuracy under harmonic excitation of finite amplitude.