Continuous improvement in nanofabrication and nano-characterization capabilities have changed projections about the role that metals could play in developing the new optical devices. Surface plasmon polaritons are evanescent waves that propagate along a metal-dielectric interface. They can be laterally confined below the diffraction limit by using subwavelength metal structures, rendering them attractive to the development of miniaturized optical devices. A surface plasmon polariton refractive index sensor and filter which consist of two metal-insulator-metal (MIM) waveguides coupled to each other by a ring resonator embedded by cross structure are proposed. And the transmission characteristics of surface plasmon polaritons are studied in our proposed structure. The transmission properties of such a structure are simulated by the finite element method, and the eigenvalue wavelengths of the ring resonator are calculated theoretically. The sensing characteristics of such a structure are systematically analyzed by investigating the transmission spectrum. The results show that there are three resonance peaks in the transmission spectrum, that is, three resonance modes corresponding to the eigenvalue solutions of the first, second and third-order Bessel eigen-function equations, and each of which has a linear relationship with the refractive index of the material under sensing. Through the optimization of structural parameters, we achieve a theoretical value of the refractive index sensitivity (S) as high as 1500 nm/RIU, and the corresponding sensing resolution is 1.3310-4 RIU. More importantly, it is sensitive to none of the parameters of our proposed structure, which means that the sensitivity of the sensor is immune to the fabrication deviation. In addition, by the resonant theory of ring resonator, we find a linear relationship between the resonance wavelength and the radius of ring resonator. So the resonance wavelength can be easily manipulated by adjusting the radius and refractive index. In addition, the positions of transmission peaks can be easily modulated by changing the radius of the ring, which can be used to design band-pass filter for a large wavelength range. Moreover, the transmission intensity and the transmission bandwidth decrease as spacing distance between the MIM waveguide and ring cavity increases. These results would be helpful in designing the refractive index sensor of high-sensitivity and band-pass filters, and have guiding significance for biological sensor applications.