Linear tunability has important applications since it can be realized by using linear control voltage and can be used conveniently without requiring nonlinear scale. In this paper, a kind of plasmonic nanostructure with a waveguide loaded with two rectangular cavities coupled by a circular cavity is proposed to produce four Fano resonance modes. The transfer matrix theory is employed to analyze the coupled-waveguide-cavity system. By analyzing the property of each single cavity, it reveals that the Fano resonances are originated from the coupling effect of the narrow modes in the metal-core circular cavity and the broad modes in the rectangular cavities. Owing to the interference of different modes, Fano peaks have different sensitivities on the cavity parameters, which can provide important guidance for designing Fano-resonance structures. Furthermore, adjusting the orientation angle of the metal core in the circular cavity can easily tune the line profile of Fano resonance modes in the structure. Especially, the figure of merit (FoM) increases linearly with the orientation angle and has a maximum of 8056. The proposed plasmonic system has the advantage of high transmission, ultracompact configuration, and easy integration, which can be applied in biochemical detecting or sensing, ultra-fast switching, slow-light technologies, and so on.