At high-speed atmospheric flights, the vehicle skin panels experience structural problems and instabilities including the panel flutter. The flutter behavior of plates laminated with variable stiffness composite plies of curvilinear fibers subjected to in-plane yawed supersonic airflow is investigated. In each variable stiffness ply, the fiber orientation changes linearly with longitude. Classical plate theory is used and the effect of aerodynamic forces is modeled by first-order piston theory. Rayleigh-Ritz method followed by eigenvalue analysis is then utilized to extract governing equations and to obtain flutter characteristics. The present formulation is verified to provide converged and accurate enough results in both flutter analysis and VSCL calculations. Effects of change in curvilinear fiber angles on flutter frequency and critical aerodynamic pressure are studied and compared to others. The results show that the critical flutter frequencies as well as the critical non-dimensional aerodynamic pressure are basically dependent on the flow yaw direction and fiber-orientation. The obtained results show the effectiveness of the method. The maximum aerodynamic pressure of the flutter is observed when the yaw air flow angle is aligned with the mid-length fiber orientation angle.