The author considers an arbitrary order (in general, nonselfadjoint) differential operator on a star-type graph consisting of a finite collection of finite segments and a single ray, all of them coming out of a single vertice. As the main spectral characteristic, a Weyl type matrix is taken, generalizing the Weyl function of the classical Sturm-Liouville operator. An algorithm for constructing a solution of the inverse problem and a uniqueness theorem are given.