A highly sensitive refractive index sensor is proposed that consists of a silicon ring surrounding a cavity in a circular photonic crystal (CPC). The bandgap of the CPC is determined from the transmission spectra. Relationships between the performance parameters and the structure parameters of the sensor are investigated. Transmission spectra of the optimized sensor filled with different analytes are analyzed, and a sensitivity of 1054 nm/RIU (refractive index units) and a quality factor of 18,206 are obtained. This work is expected to facilitate the application of sensors based on CPC.