Jean Shaw Murray, 58, publisher of the Social List of Washington, which is commonly known as the Green Book for its psuedo-suede green covers, died of a brain hemorrhage June 24 at her home in Kensington.

Mrs. Murray became publisher of the Green Book in 1977 after the death of her mother, Carolyn Hagner Shaw, who had been publisher since 1943. The Green Book was first published in 1930 by Mrs. Murray's grandmother, Helen Ray Hagner.

It consists of an annual listing of about 5,000 names that make up Washington's political and social hierarchy and for many years its release provoked an outburst of controversy, most frequently about the names that were dropped or not included.

Every year hundreds of names were added to the Green Book and a like number dropped for reasons ranging from death to moving out of town to involvement in a messy divorce or being named in a criminal indictment. A secret committee of three to five people was said to have made the final decisions on whom to include and leave out.

"I think being in the Green Book is certainly a status symbol," observed Mrs. Murray upon publication of the 1982 edition. "But it's only really important to those who are active in society."

The Green Book also includes a protocol service that provides subscribers with information such as the correct seating at dinner parties and the proper way to address a message to a deputy assistant undersecretary. It includes a telephone service that subscribers can call for answers to detailed questions.

A native Washingtonian, Mrs. Murray was a graduate of the Maret School and she attended Montgomery College.

She married a Navy officer, Thomas J. Murray Sr., and accompanied him to various posts throughout the country. In 1959 she returned to the Washington area when her husband retired from the Navy as a lieutenant commander.

Mrs. Murray went to work on the Green Book in 1976, the year before she became publisher.

In addition to her husband, she is survived by two daughters, Carolyn Knowlden of Silver Spring and Elizabeth Chwirut of Ellicott City, Md.; three sons, Thomas J. Jr., of Denver, John, of Ashton, Md., and Peter, of Chevy Chase; a brother, John F. Shaw of Bethesda, and three grandchildren.