Virtual 3-manifolds were introduced by Matveev in 2009 as natural generalizations of classical 3-manifolds. In this paper, we introduce a notion of complexity for a virtual 3-manifold. We investigate the values of the complexity for virtual 3-manifolds presented by special polyhedra with one or two 2-components. On the basis of these results, we establish the exact values of the complexity for a wide class of hyperbolic 3-manifolds with totally geodesic boundary.