The move was announced by the party's welfare spokeswoman Jackie Baillie a day after the Scottish Government failed to take forward proposals in its legislative programme.
The member's bill will be based on plans drawn up by the Govan Law Centre, which would prevent councils and housing associations from evicting tenants who fell into arrears as a result of changes to housing benefit.
The bedroom tax, as it is known, has cut benefits for tenants deemed to have a spare room by 14%Labour's bill is part of a three-pronged bid to assist tenants, thousands of whom are struggling to afford their rent. The party will call for a £50m package to support tenants when talks over the Government's 2014/15 budget begin later this year.
Meanwhile Labour-led councils across Scotland made a commitment not to evict tenants genuinely unable to pay their rent as a result of the benefit cuts. An estimated 80,000 Scots, many disabled, have been affected by the bedroom tax.
A spokesman for Finance Secretary John Swinney said: "We will take no lessons from Labour on the bedroom tax. They cannot hide from their failure to commit to scrapping it. The SNP will scrap the bedroom tax within a year of independence."