Adhesively bonded scarf repairs are the preferred method for repairing laminated composite structures, limited mainly by the amount of material removal associated with scarfing. In addition to the high strength restoration, scarf repairs also enable recovery of the original external surface as required by aerodynamic and/or external mould line considerations. In this investigation, an optimization method has been developed for determining the optimum scarf repair angles, adhesive thickness and scarf patch material for a given biaxial loading condition. The scarf angle, adhesive thickness and scarf patch material was considered by adaptive response surface method (ASRM). The optimum and near-optimum scarf repair model are presented and discussed with respect to computational model using the finite element method. As a result, boron fiber scarf patch is the best with optimal matching modulus. When the scarf angle and adhesive thickness increased, the instability load also increased, then went into their matching zone, the instability load got its maximum value quickly. Once the value of scarf angle and adhesive thickness went out of their optimal matching zone, the instability load reduced soon. Meanwhile the matching between scarf repair patch material and the parent structure material is very important. It reveals that the ASRM method can realize the stability optimization of scarf repaired laminates with high efficiency.