Signature-based algorithm including F5,GVW are efficient algorithm for computing Gro ̈bner in commutative polynomial rings. In this paper we mainly presented an signature-based algorithm for computing a Gro ̈bner basic of a polynomial ideal in which the coefficients of monomials in polynomials are taken from a Euclidean domain. The proposed algorithm is quite different from the more general algorithm reported in the literature. We combine the S-polynomial which used in the classical algorithm to the signature. Besides, the top-reduction which we used is based on a natural way of using Euclid’s division algorithm on the coefficients in the polynomials. What is more, we can get the Gro ̈bner basic of the syzygy modules of the leading terms of the ideal simultaneously.