The present work primarily deals with the study of the influence of internal moving pulsatile fluid on the dynamic stability of cantilever based single-walled carbon nanotubes considering the modified couple stress elasticity theory and the Timoshenko beam model. The axial fluid speed is characterized as simple harmonic variation about a constant mean speed. The second order method of multiple scales is employed in order to determine the closed-form expressions for the instability regions subjected to parametric resonance condition. The influences of the length scale parameter, Poisson's ratio, aspect ratio of SWCNTs, and the amplitude of static and dynamic components of the flow velocity, on the parametric instability regions are investigated. These results obtained from perturbation analysis are verified by solving the temporal equation using numerical technique.