He attended Cairo University, graduating with a degree in dentistry in 1979.
He became president of the General Union of Palestinian Students in 1974. In 2005, he was succeeded by Riyad H. Mansour, when he became Foreign Affairs Minister in the Palestinian Authority Government of February 2005. Nasser served as United Nations Deputy Special Representative of the Secretary-General for Afghanistan in the United Nations Assistance Mission in Afghanistan (UNAMA).
Al Qudwa was appointed deputy to Kofi Annan, then special envoy to Syria for the U.N. and Arab League in March 2012. He was responsible for the contacts with Syrian opposition groups. In 2014, Al Qudwa resigned from his position as U.N. Deputy Mediator on Syria.
Al Qudwa currently lives in New York City. Al Qudwa is the head of the Yasser Arafat Foundation.
Al Qudwa is a former Palestinian Foreign Minister and a member of Fatah. Al Qudwa joined Fatah in 1969. He is also a central-committee member of Fatah.
Then became an executive member of the Palestinian Red Crescent shortly after.