The nature of the progenitors of type Ia supernovae (SNe Ia) remains a mystery. Binary systems consisting of a white dwarf (WD) and a main-sequence (MS) donor are potential progenitors of SNe Ia, in which a thermonuclear explosion of the WD may occur when its mass reaches the Chandrasekhar limit during accretion of material from a companion star. In the present work, we address theoretical rates and delay times of a specific MS donor channel to SNe Ia, in which a helium (He) star + MS binary produced from a common envelope event subsequently forms a WD + MS system without the He star undergoing mass transfer by Roche lobe overflow. By combining the results of self-consistent binary evolution calculations with population synthesis models, we find that the contribution of SNe Ia in this channel is around 2.0 × 10-4 yr-1. In addition, we find that delay times of SNe Ia in this channel cover a range of about 1.0-2.6 Gyr, and almost all SNe Ia produced in this way (about 97%) have a delay time of 1 Gyr. While the rate of SN Ia in this work is about 10% of the overall SN Ia rate, the channel represents a possible contribution to the old population (1-3 Gyr) of observed SNe Ia.