A domain decomposition algorithm for material and displacement discontinuity problems in meshless method is presented. The domain is decomposed into sub-domains along the discontinuous interface. The continuity of the displacements on the interface is satisfied through the introduction of two transformation matrixes. The partitioned-matrix method is proposed to calculate the transferred stiffness matrix，which is sparse and bandy. By means of coupling meshless method and finite element method, the essential boundary condition can be imposed directly. The computer program based on the presented method is developed and two numerical examples, a beam consisted with two kinds of materials and an edge-cracked plate under uniform tension, are employed to demonstrate the correctness and efficiency of the method.