We construct a gauge theory based on nonlinear Lie algebras, which is an extension of the usual gauge theory based on Lie algebras. It is a new approach to generalization of the gauge theory. The two-dimensional gravity is derived from nonlinear Poincaré algebra, which is the new Yang-Mills-like formulation of the gravitational theory. As typical examples, we investigate R 2 gravity with dynamical torsion and generic form of "dilaton" gravity. The supersymmetric extension of this theory is also discussed.