Abstract: Based on the direct local radial basis function collocation method (LRBFCM), the band structure calculation algorithm for the anti-plane elastic wave of the cracked phononic crystals is proposed. The band structure characteristics are analyzed, and the accuracy and validity of the numerical results are verified with the comparison of the finite element method analysis. For the boundary collocation nodes, the direct method is adopted to select local nodes along the normal direction to solve the problems of stability, and the influence of the processing techniques of the numerical methods on the results is discussed. The applicability of the method for calculating the band structure of cracked phononic crystals is verified by considering different acoustic impedance ratios, scatterer shapes (square, circular) and crack conditions. The effects of shape parameters and the number of point numbers on the calculation results are investigated. Finally, the effects of crack of different length and its location on the band structure of phononic crystals are analyzed comprehensively, and a comparative analysis is carried out. The innovation of this paper is to solve the problem of calculating the band structure of cracked phononic crystals by the direct method of local radial basis function collocation method, which greatly increases the application value of phononic crystals. The results in this work show that due to the crack propagation, the bandgap of the phononic crystals structure gradually narrows; When the crack expands to a certain extent, the number of bandgaps in the phononic crystals of aurum scatterers increases, and the new bandgaps widen with the expansion of the crack. However, the number of bandgaps in the phononic crystals of aluminum scatterers decreases; The direct local radial basis function collocation method can improve the calculation efficiency and the computational accuracy significantly for the band structure of cracked phononic crystals.