Ring resonator fabricated on a silicon-on-insulator is versatile in optical integration, which can be used to realize filters, modulators and switches. However, silicon-on-insulator is difficult to control the polarization dependence, and thus its application is greatly limited. The polarization dependence of the ring resonator is caused mainly by two factors: the coupling coefficients of the coupling region at the same wavelength for the two orthogonal polarization modes are different, and the birefringence effect of curved waveguide results in the different resonant wavelengths of TE and TM polarization modes. When the coupling region polarization independence and the resonant wavelength polarization independence are simultaneously satisfied, the polarization independence of the ring resonator can be realized. In this paper, a new type of polarization-insensitive ring resonator on a silicon-on-insulator is designed based on subwavelength grating and sandwiched structure. Firstly, by adjusting the duty cycle of the subwavelength grating and the refractive index of SiN_x in the coupling region, polarization independence of the coupling region is achieved. Secondly, the refractive index of SiN_x in curved waveguides is designed to make the resonance wavelengths for orthogonal polarization modes equal. Thirdly, the parameters of the coupling region are optimized to reduce the insertion loss. The three-dimensional finite-difference time-domain method is used for simulation. The results show that the radius of the ring is only 10 μm, the 3-dB bandwidth of the device is less than 0.8 nm, and the insertion loss is lower than 0.8 dB. It has potential applications in the future dense wavelength division multiplexing systems.