Accretion induced collapse (AIC) may be responsible for the formation of some interesting neutron star binaries (e.g., millisecond pulsars, intermediate-mass binary pulsars, etc). It has been suggested that oxygen-neon white dwarfs (ONe WDs) can increase their mass to the Chandrasekhar limit by multiple He-shell flashes, leading to AIC events. However, the properties of He-shell flashes on the surface of ONe WDs are still not well understood. In this article, we aim to study He-shell flashes on the surface of ONe WDs in a systematic approach. We investigated the long-term evolution of ONe WDs accreting He-rich materialwith various constantmass-accretion rates by time-dependent calculationswith the stellar evolution codeModules for Experiments in Stellar Astrophysics (MESA), in which the initial ONeWD masses range from 1.1 to 1.35 M-circle dot. We found that the mass-retention efficiency increases with the ONe WD mass and the mass-accretion rate, whereas both the nova cycle duration and the ignition mass decrease with the ONe WD mass and the mass-accretion rate. We also present the nuclear products in different accretion scenarios. The results presented in this article can be used in the future binary population synthesis studies of AIC events.