In this paper, an efficient computational approach based on refined plate theory (RPT) including the thickness stretching effect, namely quasi-3D theory, in conjunction with isogeometric formulation (IGA) is proposed for the size-dependent bending, free vibration and buckling analysis of functionally graded nanoplate structures. The present novel quasi-3D theory not only possesses 4 variables as refined plate theory but also accounts for both shear deformation and stretching effect without any requirement of shear correction factors (SCFs). The size-dependent effect is taken into account by nonlocal elasticity theory. Isogeometric analysis shows a great advantage in dealing with the high continuity and high order derivative requirements of the displacement fields used in quasi-3D and nonlocal theory. The reliability and accuracy of the present method are ascertained by comparing the obtained results with other published ones. Numerical examples are also performed to show the significance of nonlocal effect, material distribution profile, aspect ratios and boundary conditions on the behaviour of FGM nanoplates. •We present an efficient computational approach for size-dependent behaviour of FGM nanoplates.•Both shear deformation and thickness stretching effect are taken into account by a novel quasi-3D theory with only 4 variables.•Nonlocal theory that requires third order derivatives of displacement variables is used to capture the size-dependent effect.•NURBS-based isogeometric analysis can handle properly the high-order derivative requirements.•The numerical results show reliability and effectiveness of the present method.