Addressing the party's conference in Manchester, Grayling said: "Right now virtually anyone can get a licence to sell alcohol. We will change that. We'll give communities a right of veto over new licences in their area, and councils will be able to restrict opening hours."
He promised strict penalties for off licences that break the rules, including bigger fines if they sell alcohol to under 18s. "If they do it again, we'll close them for a few days as a penalty, and if it still happens, we'll strip them of their licence permanently," he added.
Grayling said the Tories would tackle the problem of "14-year-olds hanging around with bottles of super-strength beers or ciders" by introducing big increases in the tax on strong lagers and alcopops.
Supermarkets would be banned from selling alcohol below cost price, he added.
The Association of Convenience Stores (ACS) expressed its concern over the proposals, saying they could lead to unnecessary cost and confusion among retailers.
"Retailers have already gone through a period of significant upheaval following the introduction of the recent Licensing Act," said chief executive James Lowman.
"There are already extensive penalties that local councils and communities can use to punish and deter retailers who break the law on underage sales. We think that the current laws could be made to work better rather than creating new ones."