Royal Troon is to hold a special meeting on 1 July to propose the introduction of women members.
The Scottish club said a recent consultation found that admitting women members was supported by over three-quarters of those who participated.
Muirfield voted in May not to admit women members and lost its right to stage the Open Championship.
Royal Troon, situated in South Ayrshire, is the host for this year's Open, which runs from 14-17 July.
Troon said in January it would review of its male-only membership policy.
Club captain Martin Cheyne said: "Recently we spoke about the need for our club to reflect the modern society in which we exist.
"I am pleased that a large majority of members who responded to our survey agree and support opening the club to women."
Muirfield's vote to change its rules and allow women fell short of the required two-thirds majority.
As well as provoking an Open ban, the decision received widespread condemnation from players, administrators and politicians.
World number three and former Open champion Rory McIlroy said: "It's more of a loss to Muirfield than it is to us."