Aiming to better understand how the presence of both structural and aerodynamic nonlinearities affect the aeroelastic behavior of laminated composite panels in transonic flow, we employ fluid-structure coupling algorithm with a midpoint serial staggered procedure to solve nonlinear aeroelastic responses. In this algorithm, the Euler equations are solved by a flux splitting scheme to obtain unsteady aerodynamic pressure in case of shock movement; a finite element co-rotational formulation, as well as stress-strain relations in the laminate coordinate system, is applied to model geometric nonlinear composite structure; the algorithm is validated by aeroelastic response analysis of a flat panel in the transonic and supersonic regime. Then six different thin laminated composite panels, which have two different layer orientations, cross-ply [0°/90°/0°/90°/0°] and angle-ply [45°/-45°/45°/-45°/45°], as well as three different sizes of curvature, H/h = 0, H/h = 5 and H/h = 10, are numerically simulated at Mach 1.01. The results, comprising the static divergence, flutter onset, amplitude, and spectra of the post-flutter responses are determined. They illustrate that with different layer orientation and curvature, the aeroelastic response of the composite panel presents entirely different forms. Especially, due to the development of the multiple-shock structure in the transonic regime, oscillations with very low-frequency are observed for the curved composite panels with ply [45°/-45°/45°/-45°/45°], which have not as yet been found in the work of previous researchers.