Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain Omega of IRd, d >= 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a nonconforming discretization and give numerical asymptotic behavior of the error reduction produced by the generated mesh.