The organization began in 1932 as the Greenville Community Concert Association (GCCA) with George Wrigley as President, hosting a series of concerts annually for the Greenville community. Before the Greenville Memorial Auditorium was completed in 1959, performances were held in the Ramsay Auditorium on the Woman's College of Furman University campus, or the Parker High School auditorium.

On November 10, 1969, the GCCA merged with Furman University’s Fine Arts Series, which began in 1960, to create the Furman-Greenville Fine Arts Association (FGFAA). Furman University provided the McAlister Auditorium as a concert venue, an office for the Association, and eight members of the twenty-four person board, the remaining members to come from the GCCA board.

The FGFAA continued to sponsor the annual Fine Arts Series, whose season ranged from June to May and included an average of four performances by a variety of individual artists and groups, from vocalists to symphonies. Concerts typically took place during the winter and early spring months, with artist selection as well as membership, publicity, and advertising campaigns occurring in the surrounding months. From 1987 to 1990, the Association produced a newsletter titled Bravo, which included previews and reviews of the performances from each season during those years.

With construction of the Peace Center for the Performing Arts in downtown Greenville and plans to present their own arts series beginning in 1990, the FGFAA decided to cease their series. At the final meeting on March 20, 1990, the members of the board carried out procedures to dissolve the organization following the conclusion of the 1989-1990 concert series.

In his closing address to the Association on May 20, 1990, President John Crabtree commended the organization that “brought to the stages of old Textile Hall, Ramsay Auditorium, Greenville Memorial Auditorium, and McAlister Auditorium the world’s greatest orchestras and their renowned conductors, stars of the opera, vocal and instrumental recitalists, and dancers.” The board were presented with Certificates of Appreciation for outstanding service to the arts and voted to establish an endowment at Furman University to provide scholarships for junior year students majoring in the performing arts. A plaque in recognition of the FGFAA and its contributions to the fine arts community at Furman is located in the lobby of McAlister Auditorium.