A nanoscale metal ring resonator with a notch is proposed, in which the propagating characteristics of surface plasmons was studied with the help of finite-difference time-domain method. Influences of the length and position of the notch and the radius of the ring on the transmission properties of the ring resonator have been studied in detail. We found that, compared with the ring resonator without notch, the intrinsic mode of the ring resonator will split when the length and position of the notch satisfy some special conditions. In addition, the split modes will shift toward longer wavelengths as the radius of the ring increases, while the variation of the radius has no influence on the splitting behavior of the intrinsic modes.