Also I got this in Wikipedia, Credit goes to them.
Invasion of Mongol
In 1231, Mongolians under Ögedei Khan invaded Goryeo, as part of a general campaign to conquer China. The royal court moved to Ganghwa Island in the Bay of Gyeonggi, in 1232. The military ruler of the time Choe U insisted on fighting back. Goryeo resisted for about 30 years but finally sued for peace in 1259.
Meanwhile, the Mongols began a campaign from 1231 to 1259, that ravaged parts of Gyeongsang and Jeolla provinces. There were six major campaigns : 1231, 1232, 1235, 1238, 1247, 1253; between 1253 and 1258, the Mongols under Jalairtai launched four devastating invasions in the final successful campaign against Korea, at tremendous cost to civilian lives throughout the Korean peninsula, ultimately resulting in Korea becoming a tributary of the Mongol Yuan Dynasty.
Civilian resistance was strong, and the Imperial Court at Ganghwa attempted to strengthen its fortress. Korea won several victories but the Korean military could not withstand the waves of invasions. In 1236, Gojong ordered the re-creation of the Tripitaka Koreana, destroyed during the 1232 invasion. This collection of Buddhist scriptures took 15 years to carve on some 81,000 wooden blocks, and is preserved to this day. In March 1258, the dictator Choe U was assassinated by Kim Jun. Thus, dictatorship by his military group was ended, and the scholars who had insisted on peace with Mongolia gained power. Eventually, the scholars sent an envoy to Mongol, and a peace treaty was contracted between Mongol and Goryeo. Some military officials who refused to surrender formed the Sambyeolcho Rebellion and resisted in the islands off the southern shore of the Korean peninsula.[1].
The treaty permitted the sovereign power and traditional cultures of Goryeo, and implied that the Mongols gave up controlling Goryeo under Mongolia's direct rule[2] Mongolia had annexed the northern provinces of Korea after the invasions and incorporated them into their empire. After the peace treaty with Goryeo, the Mongols planned to conquer Japan by allying with Goryeo troops; in 1274 and 1281 the Japan Campaign took place, however, failed due to a heavy storm (called the Kamikaze) and strong military resistance.
Beginning with King Wonjong, Korea was tributary of the Mongol Yuan Dynasty. Goryeo had sent 36 tributary missions to the Yuan court during the reign of Kublai Khan.[3] The Goryeo Dynasty survived under Mongolian influences until King Gongmin began to push Mongolian garrisons back around 1350. By the 1350s Goryeo regained its independence.
Here is the official link: http://en.wikipedia.org/wiki/Goryeo