The novelty of this article is to investigate the dynamic behavior and response of armchair and zigzag carbon nanotubes (CNTs) under the dynamic moving load using a bottom to up modeling nano-mechanics theory. CNTs are modeled as a Timoshenko beam structure with shear deformation effect, and the size influence of CNTs imposed using the doublet mechanics theory. Hamiltonian principle is used to derive the modified equation of motion and nonclassical boundary conditions of CNTs under moving loads. Analytical Navier method solution for simply supported CNTs beam and Newmark time integration method are developed to predict the response of the structure in time-domain. The proposed model is verified and proved with previously published works for free vibration. Parametric analysis is performed to illustrate the influence of doublet length scale, structures of CNTs, load velocities, and mass of the load on the dynamic responses of CNTs. The proposed model is useful in designing and analyzing of MEMS/NEMS, nano-sensor, and nano-actuator manufactured from CNTs.