The present paper deals with the dynamic behavior of nano-column subjected to follower force using the nonlocal elasticity theory. The nonlocal elasticity theory is used to analyze the mechanical behavior of nanoscale materials. The used method of solution is the Differential Quadrature Method (DQM). It is shown that the nonlocal effect plays an important role in the vibrational behavior of nano-columns. The results can provide useful guidance for the study and design of the next generation of nanodevices and could be useful in biomedical and bioengineering applications as well as in other fields related with the nanotechnology.