Gibson was a graduate of North Carolina A&T State University and Meharry Medical College. He served as president of the NAACP's regional branch in Greenville, South Carolina before succeeding Margaret Bush Wilson as national chairperson. As chair, he encouraged voter registration and worked to increase economic opportunities for African Americans. However, his handling of finances was controversial, and the NAACP found itself with a $4 million deficit in 1995. That year, NAACP board members voted 30-29 to replace Gibson with Myrlie Evers-Williams, widow of Medgar Evers.
Gibson died of cancer at the age of 69.