Micheál Martin would become the next Taoiseach if a general election were held tomorrow.
A new poll in the Irish Daily Mail says support for his party Fianna Fáil is at 31% - up 7 points since last spring's vote.
When people were asked who they would back, Fine Gael and Enda Kenny got just 28% support.
Sinn Féin remain unchanged at 16%, Labour were down 1 to 6%, while the AAA-PBP were up 1 to 4%.
The figures come from research firm 'Ireland Thinks' who interviewed a random sample of over a thousand adults last month.