A projective nonsingular plane algebraic curve of degree $$d\ge 4$$ d ≥ 4 is called maximally symmetric if it attains the maximum order of the automorphism groups for complex nonsingular plane algebraic curves of degree $$d$$ d . For $$d\le 7$$ d ≤ 7 , all such curves are known. Up to projectivities, they are the Fermat curve for $$d=5,7$$ d = 5 , 7 ; see Kaneta et al. (RIMS Kokyuroku 1109:182–191, 1999) and Kaneta et al. (Geom. Dedic. 85:317–334, 2001), the Klein quartic for $$d=4$$ d = 4 , see Hartshorne (Algebraic Geometry. Springer, New York, 1977), and the Wiman sextic for $$d=6$$ d = 6 ; see Doi et al. (Osaka J. Math. 37:667–687, 2000). In this paper we work on projective plane curves defined over an algebraically closed field of characteristic zero, and we extend this result to every $$d\ge 8$$ d ≥ 8 showing that the Fermat curve is the unique maximally symmetric nonsingular curve of degree $$d$$ d with $$d\ge 8$$ d ≥ 8 , up to projectivity. For $$d=11,13,17,19$$ d = 11 , 13 , 17 , 19 , this characterization of the Fermat curve has already been obtained; see Kaneta et al. (Geom. Dedic. 85:317–334, 2001).