Laya Healthcare, which has around 500,000 customers, will raise prices by an average of 6pc from July.
The insurer raised rates in January and April this year.
Around half of its plans are set to be impacted by the rise.
Chief executive Dónal Clancy blamed the move by the Government to allow public hospitals to charge insurers whenever members use a State hospitals, if they sign a waiver form.
This has seen the cost of claims from State hospitals rise by 38pc, he said.
“The sustained cost implications of the public beds re-designation charge is being felt by every health insurance provider in the market.
“ These charges will continue to drive the cost and volume of public hospital claims, with a negative knock-on impact on the cost of health cover”, Mr Clancy added.
State-owned health insurer VHI has reported last week that it made bumper profits, just weeks after imposing a new price rise on its one million members.
The increase in premiums at the start of this month was the second in the past six months.
The company said it had made a net surplus of €56.4m last year.
Next month Irish Life Health is to raise its prices by an average of 3.2pc. But some plans will go up by double this amount.
The costs for a family of two adults and two children could increase by between €100 and €250, depending on the Irish Life Health plan held.
Both Laya and VHI have already increased their rates twice in the last six months.
Meanwhile, there has been another rise in the number of people with health insurance.
New figures show that 2.15 million people now have health insurance.
This is up 30,000 from a year ago, according to figures from the Health Insurance Authority, the regulator for the sector.
Another 102,000 people have cash plans, which pay them money if they have to go to hospital or to a GP but do not cover the cost of the medical procedures.
The average premium for an inpatient health policy is now €1,177. This is up by €4 from the average premium paid in 2015.
However, it is down slightly from the cost of the average premium paid in 2014.
Some 46pc of the population now has health insurance.
The market is still below its peak level, which it reached in 2008 when 2.3 million people had private medical insurance.
The growing numbers taking out health cover is despite constant rises in the cost of cover.