John A. (Jack) Jones Jr., 56, a Foreign Service officer with the International Communication Agency, died of cancer Friday in the National Cancer Institute branch at the Veterans Administration Hospital here.

With the Voice of America in Washington for the past five years, he was a member of the policy application staff at the time of his death. Earlier he had been chief of the European division of VOA.

Since joining the State Department in 1949, Mr. Jones had served in information and cultural positions in Lagos, Nigeria, Bonn, Dusseldorf and Cologne, Germany, Stockholm, Sweden, Monrovia, Liberia, and Sofia, Bulgaria.

Interspersed with his tours of duty overseas were two earlier assignments in Washington. He was fluent in four foreign languages, Swedish, Russian, German and Bulgarian. He held a Meritorious Service Award.

Mr. Jones was born in Kemmerer, Wyo., and grew up in Charlotte, N.C. He was a student at the University of Chicago when he entered the Army Signal Corps during World War II as a photographer.

He photographed major compaigns in the European theater and after the war worked as a photographer for Esso, making several films. He then returned to the University of Chicago, and received a degree in international relations in 1949.

An accomplished violinist, he played with a number of community symphony orchestras in this country and abroad. He also had received awards as a student symphony conductor.

Mr. Jones was a model railroad buff and had built an extensive rail system at his home in Arlington.

He is survived by his wife, Ruth, a daughter, Melissa, and a son, Gregory, of the home, and his mother, Bleeker M. Shaw, of Charlotte.

The family suggests that expressions of sympathy be in the form of contributions to the American Cancer Society. CAPTION: Picture, JOHN A. JONES JR.