A plasmonic nano-sensor is proposed by means of Fano resonance in a metal-insulator-metal (MIM) waveguide structure, which consists of two identical slot cavities placed nearby two symmetrical grooves in a MIM bus waveguide. Due to the interaction of the broad bright mode and the narrow dark mode caused by the grooves and the side-coupled slot cavities, respectively, the transmission spectrum possesses a sharp asymmetrical profile. The spectral line shape can be manipulated by changing the length of the grooves, and the wavelength of the resonance peak has a linear relationship with the length of the slot cavity. These characteristics offer flexibility to design the device. This nano-sensor yields a sensitivity of ~903 nm/RIU and a figure of merit (FOM) of ~3.1 × 105. Besides, dual Fano resonance peaks are also achieved by shifting the slot cavities away from the center of the grooves, resulting in a FOM as high as 4.6 × 105. The proposed structure may find important applications in the on-chip nano-sensing area.