Hennepin County's share of building the Green Line light-rail extension continues to grow, with commissioners on Tuesday approving another $100 million for the project.

The 5-1 vote was the 11th time the County Board amended a grant agreement with the Metropolitan Council, which is overseeing the nearly $2.9 billion project. The latest infusion is a little more than half of the county's $190 million commitment to help cover a $340 million cost overrun identified last year.

The Met Council is chipping in $150 million in federal funds to cover the rest of the shortfall.

Hennepin County and the Federal Transit Authority are the two biggest funders of the Southwest light-rail project, with both committing more than $1 billion each to the project. There also are some local and state funds helping pay for what is considered the largest infrastructure project in Minnesota history.

The county primarily uses money from a $20 per vehicle excise tax and a half-cent sales tax dedicated to transportation projects to pay for its portion.

Kevin Anderson was the only commissioner to vote against the funding increase, saying it was an important project to complete but that the additional funding was too much of a financial burden on the county. He said the money could be better used addressing other infrastructure needs.

"Hennepin County has paid its obligation," Anderson said. "It feels like it's another year, another $100 million dollars."

Board Chair Irene Fernando and Commissioners Debbie Goettel and Marion Greene all expressed their ongoing support for the project, calling it an essential part of the county's climate, transit and equity goals.

"I share the frustration," Goettel said, noting that many infrastructure projects across the country have experienced cost overruns. "We've found a way to keep moving forward."

The 14.5 new miles of the Green Line between downtown Minneapolis and Eden Prairie have been plagued by cost overruns and delays. When the project was approved for federal funding in 2011, the Met Council estimated it would cost $2 billion and be operational by 2018.

The light-rail line is anticipated to be operational by 2027, and the latest price tag is $2.86 billion, with a final figure expected this spring.

The state Legislative Auditor, a government watchdog, has probed the project several times, with its most recent report released last summer. It has criticized the Met Council's management of the project and its oversight of contractors.