The supergravity is formulated as a gauge theory with the Yang–Mills Lagrangian quadratic in curvature. To arrive at such a description, the super fiber bundle based on a superspace with the OSP(n/4) symmetry group is introduced. The connection in this bundle becomes the Cartan connection when OSP(n/4) is broken to SL(2,C)⊗SO(n). In the reduced bundle, this leads automatically to curvature and torsion. Explicit calculations of the Lagrangian are carried out in terms of the Cartan–Killing metrics and the curvature form for n=1 and n=8. The final theory describes the coupling of geometry to fermion fields. These fields emerge as solder forms of the Cartan connection.