This paper studies the longitudinal vibration of cone-shaped nanotubes/nanorods. The governing equation involved in the problem is a partial differential equation with variable coefficients. A widely applicable, simple and accurate integral equation method is presented to solve the above-mentioned problem. Based on the classical and nonlocal theories of elastic rods, the natural frequencies are determined for various boundary conditions. In particular, a simple approximate expression for the resonant fundamental frequency of clamped-free carbon nanotubes as longitudinal vibration mass sensor carrying a concentrated mass at the free end is derived. A comparison of our results with the previous ones using different approaches indicates that the proposed method is easy-to-implement and effective.