An improved moving least-squares (IMLS) approximation for the field variables is proposed for geometrically nonlinear large deformation analysis of functionally graded carbon nanotube (FG-CNT) reinforced composite quadrilateral plates. The plate considered is of moderate thickness and, hence, the first-order shear deformation theory (FSDT) and Von Kármán assumption are adopted to incorporate the transverse shear strains, rotary inertia and moderate rotations. The CNTs are assumed to be uniaxially aligned in the axial direction and functionally graded in the plate thickness direction. The discrete nonlinear governing equation is derived based on the IMLS-Ritz method. The modified Newton-Raphson method combined with the arc-length iterative algorithm is employed to solve the nonlinear deformation of the FG-CNT reinforced composite quadrilateral plates. Improvements in computational efficiency and elimination of shear and membrane locking are achieved using a stabilized conforming nodal integration scheme to evaluate the system's bending stiffness. Through detailed parametric studies, CNT distribution, CNTs volume fraction, aspect ratio and thickness-to-width ratio and different boundary conditions are demonstrated to effect significantly on the large deflection behaviors of the quadrilateral FG-CNT reinforced composite plates.