A periodic array of V-type opened silver tubes is proposed to serve as a refractive index sensor. The transmission properties of this structure are investigated via the finite-difference time domain method. Simulation results show that the transmission spectra of this structure have three tunable peaks when the electric field of the incident light is perpendicular to the gap. The peaks are induced by the propagating surface plasmon resonance (PSPR) at the silver-quartz interface and two different localized surface plasmon resonances (LSPR), respectively. The influences of structure parameters, such as array period, the tube diameter, height and gap width, on the transmission peak wavelength and full-width at half-maximun (FWHM) are analyzed By optimizing the structure, it can serve as a LSPR sensor with a figure of merit of 13.2.