The optical properties of cylindrical core-shell nanorods (CCSNs) are theoretically investigated in this paper. The results show that Fano resonance can be generated in CCSNs, and the wavelength and the intensity at Fano dip can be tuned respectively by adjusting the field coupling of cavity mode inside and near field on gold surface. The high tuning sensitivity which is about 400 nm per refractive-index unit can be obtained, and an easy-to-realize tunable parameter is also proposed. A two-oscillator model is also introduced to describe the generation of Fano resonance in CCSNs, and the results from this model are in good agreement with theoretical results. The CCSNs investigated in this work may have promising applications in optical devices.