No clear plans have been put in its place but it is likely to be switched to either a land or property-based tax.
A report published by a cross-party commission at the end of last year concluded that the current system should end.
The Scottish government is expected to set out its plans for reform next week.
When the Commission on Local Income Tax made its conclusions in December, Scottish Liberal Democrat leader Willie Rennie said at the time: "This report sets out plenty of alternatives for the reform of local government finance but after eight years, people might have expected more from a government that said it was committed to reforming the council tax system."
Delegates at the Scottish Liberal Democrat conference in Edinburgh have voted to drop their long standing local income tax policy.