The paper describes an application of a fictitious space technique to constructing a preconditioner for stiffness matrices generated by nonconforming finite element method on unstructured regular triangulations. Given an unstructured mesh, a structured hierarchical mesh is constructed "approximating" in certain sense the original one. Introducing special interpolation operators we reduce the problem of constructing a preconditioner in a space associated with unstructured grid to the problem of constructing one in a fictitious space corresponding to the structured grid. Within the fictitious space we apply multilevel preconditioner with local refinement.