Under the current rules, employees can earn £10,000 in a financial year before they have to start paying income tax. This has risen from £6,500 since the Coalition was elected in 2010 and is due to increase further to £10,500 in April 2015.
Under the Liberal Democrats' plans, the higher rate would be introduced by the end of the next Parliament in 2020.
Alexander hinted that the party would also look at the reforming the way that National Insurance is taken from staff's wages – although didn't offer any further details at this stage.
Alexander hailed the Liberal Democrats' part in raising the tax-free allowance since 2010, claiming the party has "fought to keep it on the agenda" throughout its term.
“Now we want to go even further and lift the amount of money people can earn before paying income tax," he said. "This will take hundreds of thousands more low earners out of tax altogether and give millions of working people a further tax cut of £400. This move will also give a tax cut to over 6 million pensioners."
He added that the plans would amount to a "generational shift" towards a fairer tax system.
"That’s the way to build a stronger economy and a fairer society and ensure that everyone has the opportunity to get on in life,” he said.