To examine the crack propagation in quasi-brittle materials, cohesive models have been suggested by the works of researcher. They treat the existence of a process zone at the crack tip, with a suitable constitutive law, linking the tensile normal stress T and the relative displacement among the two crack edges. In this paper, we employed the cohesive model which examines the mode I interlaminar fracture into stitched reinforced composite laminates. The test configuration that we used in this study was a stitched reinforced double cantilever beam samples. A bilinear damage-rate-dependent cohesive traction-separation law is implemented to design the woven composite fracture and discrete nonlinear spring elements to characterize the stitches influence, its advantages and disadvantages. A novel macroscopic law adopted from a 1D micromechanical-stitching model is invented to model the stitches effect along the interface. The numerical simulations of double cantilever beam test with the present model present a significant agreement compared to the experimental results.