Type Ia supernovae (SNe Ia) are thermonuclear explosions of carbon-oxygen white dwarfs (CO WDs), and are believed to be excellent cosmological distance indicators due to their high luminosity and remarkable uniformity. However, there exists a diversity among SNe Ia, and a poor understanding of the diversity hampers the improvement of the accuracy of cosmological distance measurements. The variations of the ratios of carbon to oxygen (C/O) of WDs at explosion are suggested to contribute to the diversity. In the canonical model of SNe Ia, a CO WD accretes matter from its companion and increases its mass till the Chandrasekhar mass limit when the WD explodes. In this work, we studied the C/O ratio for accreting CO WDs. Employing the stellar evolution code MESA, we simulated the accretion of He-rich material onto CO WDs with different initial WD masses and different mass accretion rates. We found that the C/O ratio varies for different cases. The C/O ratio of He-accreting CO WDs at explosion increases with a decreasing initial WD mass or a decreasing accretion rate. The various C/O ratios may, therefore, contribute to the diversity of SNe Ia.