A generalized spinor structure is constructed as a GL(2,) principal fiber bundle over the metric-affine manifold. Relations between vectors and spinors are established explicitly through the generalized Pauli and Dirac matrices. An expression for generalized spinor connection is obtained. The Dirac equation in metric-affine space-time is written in the form representing an interaction of spinors with nonmetricity explicitly. A possible physical meaning of nonmetrical objects is discussed in brief.