(Reuters) - Car rental company Avis Budget Group Inc <CAR.O> said it will buy Zipcar Inc <ZIP.O> for about $500 million in cash to enter the fast-growing U.S. car-sharing market.

The offer of $12.25 per share is at a premium of 49 percent to Zipcar's Monday close.

"We see car sharing as highly complementary to traditional car rental, with rapid growth potential and representing a scalable opportunity for us as a combined company," Ronald Nelson, Avis' chief executive, said in a statement.

Rising gasoline prices have driven demand for car sharing, attracting car rental companies. Enterprise Holdings Inc<EPRIH.UL>, the largest U.S. car rental company, is also expanding aggressively in the car-sharing market.

However, Zipcar has struggled to grow its presence in smaller cities to counter the threat of a saturating market in bigger cities. It is also encountering increased competition from traditional car rental companies such as Hertz Global Holdings Inc <HTZ.N> and Enterprise.

The deal, expected to close in the spring of 2013, will add to Avis' earnings, excluding items, from the second year and is expected to generate between $50 million and $70 million in annual synergies.

Avis said it expects to fund the transaction primarily with available cash and additional debt. The company had cash and marketable securities of about $554 million as of September 30.

Citigroup is advising Avis while Morgan Stanley is advising Zipcar on the transaction.

Zipcar's shares closed at $8.24 on the Nasdaq on Monday. Avis' shares closed at $19.82.

(Reporting by Sagarika Jaisinghani and Tej Sapru in Bangalore; Editing by Supriya Kurane)