Summary: A model of noncommutative gravity is constructed by means of B. Fedosov [Deformation quantization and index theory. Berlin: Akademie Verlag (1996; Zbl 0867.58061)] deformation quantization of an endomorphism bundle. The fields describing noncommutativity – symplectic form and symplectic connection – are dynamical, and the resulting theory is coordinate covariant and background independent. Its interpretation in terms of a Seiberg-Witten map is provided. Also, a new action for ordinary (commutative) general relativity is given, which in the present context appears as a commutative limit of noncommutative theory.