Vibration of various types of structures such as beam, plate, shell, and rod have been investigated by researchers for their application in a wide range of mechanical systems. The longitudinal vibration of the rods is of great interest, so that the researchers have performed them numerically or analytically and precise or approximate. In this research, the nonlinear longitudinal free vibration of rod with variable cross-section under finite strain has been investigated. First, the governing equations of the rod with variable cross-section were obtained, which are partial differential equations; then, they were transformed to nonlinear ordinary differential equations, using the Galerkin method with considering one mode shape. The problem was investigated for two boundary conditions. Using the multiple scales method, the equations were analytically solved. The differential equations are solved by Runge-Kutta numerical method of order 4, and then compared with the analytical solutions. The effect of the amplitude and rate of changing cross-section on the ratio of linear to nonlinear frequency and also the effect of different initial condition, rate of changing cross-section and coefficient of damper were shown in figure. The results show that the tapered cross-sectional area has a significant effect on the ratio of linear to nonlinear frequency to vibrations amplitude. The coefficient of damper has a little effect and initial condition has a considerable effect on the process of problem.