This study examines the vibrational behavior of numerous hetero-junctions and their fundamental CNTs under different boundary conditions. The natural frequencies of homogeneous CNTs (zigzag and armchair) were obtained analytically and through a finite element method and compared with each other. In addition, the computational results of hetero-junctions were obtained and also compared with their constituent homogeneous CNTs. It has been shown that the natural frequency of straight hetero-junction CNTs lies within the range of the values of their fundamental CNTs in the case that the wider tube fixed. In addition, it was also concluded that the eigen-values of straight hetero-junctions and their fundamental CNTs increase by increasing the chiral number of CNTs. Finally, it was also shown that the armchair CNTs are more stable in their vibration due to higher natural frequencies than zigzag configurations.