A novel one dimensional periodic dielectric ring waveguide (PDRWG) is proposed and its dispersion properties are studied in details. Based on the proposed waveguide structure, a compact dual wavelength demultiplexer is designed. By a finite-difference time-domain (FDTD) simulation method, the performance of the designed device is calculated and analyzed. The dual wavelength demultiplexer can split the communication wavelengths of 1.31 and 1.55 mm into different waveguides and output from different ports with relative high transmittances of about 98% and 92%, respectively. The PDRWG may find applications in multi-wavelength demultiplexers or other novel integrated photonic devices.