A numerical and experimental investigation for the analysis of delamination problem under mode I loading in composite material is presented. Firstly, the simulation of the delamination under mode I loading and failure of composite materials based on the cohesive segments model is investigated by using the meshfree method. With the partition of unity of moving least-squares shape functions, the discontinuities at the cohesive segments are approximated with additional degrees of freedom at the nodes. An iterative solution scheme between the continuous and discontinuous fields is presented to solve mode I delamination growth. Secondly, to verify the meshfree method's results, an experimental investigation and the finite element method were used for the simulation of delamination. The experimental study used a double-cantilever beam made of carbon/epoxy laminate (AS4/3501-6) which consists of 10 plies in (10) and [0/90/0/90/0](s) layup with delamination inserted in the middle of the laminate. The critical fracture force, which can be experimentally measured, was used to calculate the mode I delamination fracture toughness of the carbon/epoxy laminate. Results obtained from the meshfree method showed very good agreement with experimental data for single-mode delamination under mode I loading. The meshfree method could also be used effectively to produce delamination growth in composite laminates and is especially suitable for the simulation of complex delamination patterns that are difficult to model using traditional numerical methods.