  We establish Gr\"{o}bner-Shirshov bases theory for Gelfand-Dorfman-Novikov
algebras over a field of characteristic $0$. As applications, a PBW type
theorem in Shirshov form is given and we provide an algorithm for solving the
word problem of Gelfand-Dorfman-Novikov algebras with finite homogeneous
relations. We also construct a subalgebra of one generated free
Gelfand-Dorfman-Novikov algebra which is not free.
