A fluoroelastomer composition comprising (a) a fluoroelastomer having stabilized end group derived from an isoparaffin selected from the group consisting of isobutane, isopentane and isohexane, (b) at least one member selected from the group consisting of bivalent metal oxides, bivalent metal hydroxides and mixtures of bivalent metal oxide or metal hydroxide with metal salt of weak acid, (c) an aromatic polyhydroxy compound and (d) a quaternary ammonium compound of 8-alkyl- (or 8-aralkyl-)1,8-diazabicyclo[5.4.0]-7-undecenium, provides a fluoro-rubber having low compression set and excellent elastic properties and has excellent processing and storage properties. The fluoroelastomer can be cured with appropriate induction time and fast cure rate by the use of a specific curing agent system mentioned above.