A readily available β-sulfonamide alcohol-titanium complex was found to be effective on promoting the asymmetric addition reaction of an alkynylzinc reagent to unactivated simple ketones under very mild conditions. And the corresponding chiral tertiary propargylic alcohols were obtained with enantiomeric excesses of up to 86%, which provided a simple, practical and inexpensive method to generate chiral tertiary propargylic alcohols.