Pioneer residents of this area called their community Fish Creek until 1880, when a U.S. post office was established and named for the local postmaster, J.J. Murray. This cemetery dates to May 6, 1884, when the infant child of Russell and Rosa Bell Hart Tyra died and was buried on land set aside by grandparents Jesse V. and Martha Jane Higgins Tyra. A few months later, the infant child of neighbors John W. and Leona Walsh died and was buried here with the Tyra baby. J.V. and Martha Tyra officially donated the acre of land surrounding the graves for a public neighborhood graveyard in 1898. In later years, descendants of the pioneer Price and Dozier families donated additional land to increase the size of the graveyard to two acres.
Among the interments here are those of many early settlers of this area of Young County. A large number of deaths between 1900 and 1919 are believed to be due to the worldwide influenza epidemic of that time period. Also buried here are veterans of the Civil War, Spanish American War, World War I, World War II, and Vietnam. Maintained by the Murray Community Cemetery Association, the graveyard remains as a visible reminder of the community's heritage.