In this study, the aeroelastic stability and response of a swept composite wing in subsonic incompressible flow are investigated. The wing is modeled as an anisotropic tapered thin-walled beam with the circumferentially asymmetric stiffness structural configuration to establish proper coupling between bending and torsion. The structural model considers a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, nonuniform torsion, rotary inertia and three-dimensional strain effects. The aerodynamic strip method based on two-dimensional Wagner function in unsteady incompressible flow is used. Following the analysis, the mass, stiffness and the damping matrices of the nonconservative aeroelastic system are formed such that the extended Galerkin method and the separation of variables method can be employed. As a result, the coupled and linear governing system of dynamic equations is obtained. Then, by transforming matrices into the state-space and state-vector forms, the problem under study is finally converted into an eigenvalue problem. The flutter and the divergence speeds for various layer configurations with different geometric and material properties and fiber orientations are obtained. By solving the aforementioned equations of motion in the time domain, the aeroelastic responses of the tapered swept composite wing are computed. The obtained results are compared with the available literature.