This paper investigated the free vibration of simply supported single-walled carbon nanotubes(SWCNTs) with both ends restrained elastically. Based on nonlocal Euler-Bernoulli beam theory, the governing partial differential equations of motion and associated boundary conditions were derived by Hamilton’s principle. The differential transformation method (DTM) was employed to solve the equation of motion and the influences of the nonlocal parameter, the viscoelastic CNT parameter and restraining elastic coefficient on the dynamic behaviors of the SWCNT were analyzed. It can be concluded that the nonlocal small-scale parameter and the viscoelastic CNT parameter make the SWCNT natural frequency decrease. More importantly, the results show that it will be a convenient and effective way to increase the natural frequency SWCNT system through additional elastic restraining with proper coefficient on two ends while their values are low.