A modified numerical manifold method is proposed to predict crack growth of engineering materials. The first-order Taylor expansion of the displacement functions is adopted on physical patches，endowing the degrees of freedom of the physical patches with physical meanings. Enriched displacement functions used to capture stress singularity are adopted for the physical patches around the crack tip，which predicted more accurately the direction of crack propagation. Meanwhile a new algorithm for updating the physical cover system is proposed，which was more convenient and suitable for both small and large deformation problems. Numerical examples for typical linear elastic fracturing problems were presented. The results show that the predicted propagation paths are in accordance with the results obtained by others. The effectiveness and correctness of the method are thus confirmed.