Mobile Fighter G Gundam: Edge Of Gunsmoke

Rather than having a war between the colonies and the Earth, a fighting tournament is held. Called the Gundam Fight, it is held once every four years by the United Colonies Federation. Each country would send its own representative, that would pilot a Gundam, and the Gundams would then fight on the Earth until only one is left, and that Gundam's nation will then be able to obtain sovereign rights over all the nations, until another nation wins in the next Gundam Fight. This series is set in Future Century (FC) 60, during the 13th Gundam Fight and it focuses on the Neo Japan Gundam Fighter Domon Kasshu, who is in the fight as much to win as well as fulfill his own mission of tracking down his brother who had stolen a mysterious Gundam; the Devil Gundam from the Neo-Japan government.
(Source: Wikipedia)

Rather than having a war between the colonies and the Earth, a fighting tournament is held. Called the Gundam Fight, it is held once every four years by the United Colonies Federation. Each country would send its own representative, that would pilot a Gundam, and the Gundams would then fight on the Earth until only one is left, and that Gundam's nation will then be able to obtain sovereign rights over all the nations, until another nation wins in the next Gundam Fight. This series is set in Future Century (FC) 60, during the 13th Gundam Fight and it focuses on the Neo Japan Gundam Fighter Domon Kasshu, who is in the fight as much to win as well as fulfill his own mission of tracking down his brother who had stolen a mysterious Gundam; the Devil Gundam from the Neo-Japan government.
(Source: Wikipedia)

After a generation of warfare, the Gundam boys finally secured a peace between Earth and the colonies by helping to defeat the Oz and White Fang armies. Now, out of the rubble, the surviving soldiers are re-emerging and clustering together into new factions. Heero Yuy has become a vigilante pacifist, tracking down weapons stashes and destroying them, while Relena, former Queen of the Earth Sphere, tries to maintain the peace politically. But an unmanned weapons factory has been discovered somewhere near Mars, and now the boys are going to have to dust off their mechs for one more battle to save the tenuous peace. 
(Source: Tokyopop)

In the Year FC 60, much of mankind inhabits space colonies which orbit the Earth. Dominance over the colonies is decided once every four years by a large tournament in which each nation sends a single representative to fight the others with a giant robot called a Gundam. Domon Kashuu is selected to represent Neo-Japan in one of these tournaments, but he fights less to ensure his nation's victory than to find his brother, who has been blamed for the deaths of Domon's parents and the disappearance of a very dangerous weapon, the Dark Gundam or Devil Gundam.

(Source: Anime News Network)

In F.C. 60, the 13th Gundam Fight begins. Domon Kasshu pilots the Shining Gundam as the representative of Neo Japan, the Japanese space colony. Along with his crew member Rain Mikamura, he battles the other countries' representatives in order to earn the right to rule Earth and the colonies for four years for Neo Japan. However, Domon seems to be more concerned with finding his brother and the stolen Devil Gundam.