Speaking at the party conference in Glasgow, mental health spokesman Miles Briggs said he'd met with Scottish Parliament authorities and would table the bill in coming months.
Frank's Law would see free care for dementia patients extended to those under the age of 65.
It's named after former Dundee United footballer Frank Kopel, who passed away in 2014 after a battle with the illness.
His wife Amanda spoke at today's conference to outline the importance of the law change, which all parties except the SNP support.
Mr Briggs previously announced he would act if the Scottish Government failed to, particularly now there is majority support for Frank's Law within the Scottish Parliament.
Scottish Conservative mental health spokesman Miles Briggs said:
"It is a shocking indictment on this SNP government's record on health that terminally ill patients under the age of 65 are being charged for the basic help they need.
"Many patients and families have told me, when you're on your deathbed, worrying about where you'll find money to pay for vital care is the last thing you want to go through.
"That's why Frank's Law is needed today, it was needed yesterday, and I will not let the SNP kick this into the long grass.
"I've met with the Scottish Parliament's bills team, and unless the Scottish Government does something soon, I will be launching a member's bill in the summer."