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So far, the carbon nanotube (CNT) distributions have been still limited in the linear forms, which may lead to the limitations in maximizing the strength and potential of carbon nanotube reinforced composite (CNTRC) structures. This study, hence proposes a type of novel CNTs distribution for improving the stiffness of CNTRC beams. The distributions are in the nonlinear forms and ensure the same total CNT volume fraction along the thickness of structures. For demonstrating, the effectiveness of the proposed CNT distributions, the static, free vibration and buckling analyses of functionally graded carbon nanotube (FG-CNT) reinforced composite beams using the new CNT distributions are conducted and one-dimensional NURSB basis functions based on the third-order shear deformation theory (TSDT) are utilized to describe the exact geometry and to approximate the unknown solution in finite element model of the beam. The numerical investigations of the geometric and material parameters reveal that the new nonlinear CNT distributions can help increase the normalized frequency, buckling load and the nondimensional central deflection to the maxima of 8%, 16% and 16% respectively, in some conditions of geometric parameters.