Accurate and efficient fracture modeling of composites is essential for predicting failure in challenging engineering applications. Phase-field models avoid the laborious task of algorith- mically tracking discontinuities by representing interfaces via an additional continuous field i.e., the phase field that smoothly varies from zero (inside the crack) to one (away from crack). However, phase field simulations are computationally demanding; they increase the number of unknowns, require staggered solvers and necessitate fine meshes. In this work, an adaptive scaled boundary finite element method is developed with the objective of reducing this compu- tational toll without compromising accuracy. The Scaled Boundary Finite Element Method (SBFEM) has emerged as a promising alternative to standard discretization approaches effectively fusing the advantageous characteristics of the Finite Element Method and the Boundary Element Method. A salient feature of the SBFEM is its polytope nature, which only imposes the condition of star-convexity on elements. This allows for a seamless adoption of balanced quadtrees as hierarchical meshes without the need to treat hanging nodes. In conjunction with polygon clipping to treat complex boundaries, the SBFEM provides a powerful pathway to adaptively refining meshes in the vicinity of a propagating crack. In this work, we use of a cohesive phase-field model for simulating intra-laminar damage in fab- ric composite laminates. A linear crack-surface density functional is employed, which retains an elastic behaviour until damage onset. Furthermore, a quasi-quadratic degradation function which can be used to calibrate experimental strain softening curves, thereby accurately predict- ing quasi-brittle damage response in fabric composites. The nonlinear phase-field evolution equation is solved using a staggered solution scheme, and an Augmented Lagrange method is incorporated to facilitate irreversible evolution of damage phase-field variable. A set of bench- marks pertaining to Mode I and Mode II fracture is examined and the accuracy and efficiency of the proposed method is demonstrated. The research work is implemented in the framework of H.F.R.I call “Basic research Financing (Horizontal support of all Sciences)” under the National Recovery and Resilience Plan “Greece 2.0” funded by the European Union –NextGenerationEU (H.F.R.I. Project Number: 15097).