Permanent TSB customers who make lump-sum payments to their mortgage accounts of over €5,000 are going to receive bonus payments of 10% from the bank.
The offer is for all tracker mortgages, residential, investment and commercial, and is available until the middle of June.
Like other Irish financial institutions, Irish Life & Permanent is losing money on its tracker mortgage accounts so its banking arm, Permanent TSB, wants some of its 70,000 tracker customers to make overpayments.
This would enable the bank to cut its losses on funding the loans, which are costing it about €400m a year.
Trackers closely follow the rates set by the European Central Bank.
This month the ECB raised its rate to 1.25% - marking the start of what the market expects to be a series of hikes.
The recent bank stress tests showed that Irish Life & Permanent needs to raise €4bn in capital to protect it against further financial shocks.
It will be restructured and its profitable assets sold to become a small niche bank for deposits and mortgages.