Which nation gave Liberia his independent?

No nation did, per se. Liberia has never been subjected to official colonial rule by a foreign country. However, in 1821, the American Society for Colonizing the Free People of Color of the United States founded a colony there whose intent was to send free African-Americans and liberated slaves to live there (which was a source of some controversy), hence the name "Liberia." This American Colonization Society acquired rights to Monrovia, what is now the capital, and they had chief control over the country.

From my understanding, Liberia Independence Day, which was July 26, 1847, came about after the Society declined and the Liberians proclaimed their independence from the Society, and its borders expanded to what is now known as the whole nation of Liberia. Americans came to acknowledge Liberia's sovereignty.