(Reuters) - U.S. car rental company Hertz Global Holdings Inc (>> Hertz Global Holdings Inc) said on Tuesday it would replace its chief executive and reduce its board size in January, moves backed by its biggest shareholder Carl Icahn.

Hertz said CEO John Tague would retire on Jan. 2, a little over two years after he got the role with backing from Icahn, and be replaced by Kathryn Marinello, who sits on the boards of AB Volvo (>> Volvo AB) and General Motors Co (>> General Motors Company).

"Kathy has a history as a proven CEO and I believe she is the right person to lead Hertz as we move forward," Icahn, who has a 35.3 percent stake in Hertz, said in a statement issued by the company.

Hertz also said its three longest serving directors, Linda Fayne Levinson, Carl Berquist and Michael Durham, would leave the board, effective Jan. 2. The company did not say why the trio had decided to step down.

That would leave the company with seven directors, including three who were nominated by Icahn in September 2014 in return for not running a proxy contest. He had a roughly 9 percent stake in Hertz at the time and has been boosting his holding since.

The billionaire investor disclosed he had doubled his stake in Hertz on Nov. 8, the same day the stock plunged nearly 23 percent after the company cut its full-year profit forecast following a write down in the value of some of its cars.

Hertz, facing stiff competition from the likes of Uber [UBER.UL], has been gradually reducing the size of its big fleet, which it operates under brands such as Hertz, Dollar and Thrifty. It has rental agreements with Uber and Lyft.

Icahn-backed Tague was named Hertz's CEO in November 2014, fending off a challenge from Dollar Thrifty CEO Scott Thomson, who was backed by activist investor Jana Partners.

Marinello has been a senior advisor of Ares Management LLC since March 2014 and was CEO of customer management services provider Stream Global Services Inc from 2010 to March 2014.

She has worked for more than 10 years at General Electric Co (>> General Electric Company).

Hertz's shares were down about 1.5 percent at $24.75 in extended trading on Tuesday. They closed up 10.6 percent in the regular session, but are still down more than 55 percent this year.

(Reporting by Anya George Tharakan in Bengaluru; Editing by Savio D'Souza)

By Anya George Tharakan