Summary: As a first endeavor, the aeroelastic responses of functionally graded carbon nanotube reinforced composite (FG-CNTRC) truncated conical curved panels subjected to aerodynamic load and axial compression are investigated. The nonlinear dynamic equations of FG-CNTRC conical curved panels are derived according to Green’s strains and the Novozhilov nonlinear shell theory. The aerodynamic load is estimated in accordance with the quasi-steady Krumhaar’s modified supersonic piston theory by taking into account the effect of the panel curvature. Matrix transform method along with the harmonic differential quadrature method (HDQM) are employed to solve the nonlinear equations of motion of the FG-CNTRC truncated conical curved panel. The advantage of the matrix transform method is that we only need to discretize the meridional direction. Effects of semi-vertex angle of the cone, subtended angle of the panel, boundary conditions, geometrical parameters, volume fraction and distribution of CNT, and Mach number on the aeroelastic characteristics of the FG-CNTRC conical curved panel are put into evidence via a set of parametric studies and pertinent conclusions are outlined. The results prove that the panels with different FG distributions have different critical dynamic pressure. It is found that the semi-vertex and subtended angles play a pivotal role in changing the critical circumferential mode number of the flutter instability. Besides, the research shows that the superb efficiency of proposed method with few grid points, which requires less CPU time, are attributed to the matrix transform method and the higher-order harmonic approximation function in the HDQM.