The locally resonant (LR) cylindrical shell phononic crystal structure with periodically attached spring-mass resonators in the circumferential direction of cylindrical shells is proposed in this study to reduce the vibration of cylindrical shells. And the band structure of the phononic crystal shows that the two low frequency band gaps can be formed. One of the band gaps has a starting frequency as low as 650 Hz and a bandwidth of 330 Hz, and the other has a lower frequency range of 0 to 371 Hz, which is due to the coupling between the cylindrical shell and spring-mass resonators. Further, the effects of the mass ratio of the cylindrical shell to the mass, the stiffness of the spring-mass resonators and the cell width on the band gaps were analyzed. Moreover, the characteristics of the vibration transmission in finite LR cylindrical shells verify the vibration suppression in the band gap for the locally resonant cylindrical shell phononic crystal. Finally, the research results provide a theoretical reference for the vibration reduction of cylindrical shells.