Abstract: The phase-field method can automatically capture crack initiation and propagation, which has obvious advantages in simulating complex fracture behaviors in composites. To distinguish different fracture modes in fiber-reinforced composites (FRC), two phase-field variables were introduced to represent the damage evolution of fiber and matrix, respectively. An adaptive mesh refinement scheme based on the quadtree decomposition was incorporated into the anisotropic double phase-field formulations using the phase-field variables as the error indicators. The corresponding Matlab programs were designed and developed to study the fracture behaviors of the unidirectional and variable stiffness fiber-reinforced composite single layer laminate under tensile load. The results show that: The numerical results are in good agreement with the experimental results; and the adaptive double phase-field method can not only guarantee high computational accuracy but also refine the mesh along the crack paths with the evolution of phase-field parameters automatically and accurately. Moreover, this method can simplify the mesh pre-processing process, greatly reduce the number of unnecessary elements and the calculation cost, improve the calculation efficiency.