In this paper, basic properties of the Gröbner bases for modules in Z[x]^n are given. Based on these properties, two algorithms to compute the Gröbner bases for modules in Z[x]^n are proposed. The first one is based on the Hermite normal form computation on Z^n and the idea of the F4 algorithm. The second one is a modular algorithm. Unlike the traditional modular algorithm, here we use the unlucky primes. Experimental results show that these two algorithms are more efficient than the Buchberger style algorithm.