Pedra Branca is located in the eastern entrance of Singapore Strait in South China Sea, 7.7 miles south from Johor of Malaysia Peninsula, 25.5 miles east from Singapore 7.6 miles north from Bidan islands of Indonesia. Its geographical location is N. 1° 19' 48" and E. 104° 24' 27". There is an island located in 250 meters of the separated two strings approximately 0.6 miles south from Pedra Branca called Middle Rock, and a low-tide elevation named South Ledge located in 2.2 miles southern west away from Pedra Branca. The Johor has owned the historical title over Pedra Branca. But over 150 yeas till now, Singapore has operated the Horsburgh Lighthouse in Pedra Branca and claims itself as the sovereign authority without any objection. On 21 Dec 1979, a official map issued by the authority of Malaysia has cover the Pedra Branca within its territorial sea which caused Singapore severe rejection over the map and ask for its correction through diplomatic means in 14 Feb 1980 but afterwards failed and the sovereign dispute over Pedra Branca has its commence. In 1994, both States agreed to submit the sovereign dispute to the International Court of Justice, and in Feb 2003 the Special Agreement was concluded and submitted to the Court. On 23 May 2008, the Court declares that the sovereignty over Pedra Branca is belonged to Singapore, while Middle Rock belongs to Malaysia and the sovereignty over the South ledge is belonged to the State where it located in its territorial sea. This article has put its effort on the sovereign dispute is concerning the material issue under international law including the historical title, occupation on terra nullius, prescription, estoppels and the lost of sovereignty by acquisition of its original authority.