A kind of plasmonic structure consisted of an equilateral triangle-shaped cavity (ETSC) and a metal-insulator-metal (MIM) waveguide is proposed to realize triple Fano resonances. Numerically simulated by the finite difference time domain (FDTD) method, Fano resonances inside the structure are also explained by the coupled mode theory (CMT) and standing wave theory. For further research, inverting ETSC could dramatically increase quality factor to enhance resonance wavelength selectivity. After that, a bar is introduced into the ETSC and the inverted ETSC to increase resonance wavelengths through changing the structural parameters of the bar. In addition, working as a highly efficient narrowband filter, this structure owes a good sensitivity (S = 923 nm/RIU) and a pretty high-quality factor (Q = 322) along with a figure of merit (FOM = 710). Additionally, a narrowband peak with 1.25 nm Full-Width-Half-Maximum (FWHM) can be obtained. This structure will be used in highly integrated optical circuits in future.