We established a theoretical model for a single knot-ring resonator and investigated the transmission spectrum by Jones matrix. The numerical results show that two orthogonal polarization modes of knot-ring, which are originally resonated at the same wavelength, will split into two resonant modes with different wavelengths. The mode splitting is due to the coupling between the two orthogonal polarization modes in the knot-ring when the twisted angle of the twist coupler is not exactly equal to ( is an integer). It is also found that the separation of the mode splitting is linearly proportional to the deviation angle with a high correlation coefficient of 99.6% and a slope of . Furthermore, a transparency phenomenon analogous to coupled-resonator-induced transparency was also predicted by the model. These findings may have potential applications in lasers and sensors.