Employing Eggleton's stellar evolution code and assuming optically thick winds, we systematically studied the He star donor channel of Type Ia supernovae (SNe Ia), in which a carbon-oxygen white dwarf (WD) accretes material from a He main-sequence star or a He subgiant to increase its mass to the Chandrasekhar mass. We mapped out the initial parameters for producing SNe Ia in the orbital period–secondary mass plane for various WD masses from this channel. Based on a detailed binary population synthesis approach, we find that this channel can produce SNe Ia with short delay times (~100 Myr) implied by recent observations. We derived many properties of the surviving companions of this channel after SN explosion, which can be tested by future observations. We also find that the surviving companions from the SN explosion scenario have a high spatial velocity (>400 km/s), which could be an alternative origin for hypervelocity stars (HVSs), especially for HVSs such as US 708.