The generalized conditional symmetry (GCS) method is applied to a specific case of the Klein–Gordon–Fock (KGF) equation with central symmetry. We first investigate the conditions which yield the KGF equation that admits special class of secondorder GCSs. The determining system for the unknown functions is solved in several special cases. New symmetry operators and related exact solutions, different in form and structure from the ones obtained using other methods, are pointed out. Several surface plots of solutions are displayed.