The GVW algorithm is an algorithm computing Gr\"{o}bner bases for ideals in a polynomial ring over a field, which is presented by Gao, Wang and Volny in 2010. We generalize the GVW algorithm and present an algorithm to compute Gr\"{o}bner bases for ideals of polynomials over several kinds of valuation rings. We also give an dynamical Gr\"{o}bner basis algorithm over Dedekind rings based on GVW.