Let A ={a1,a2,...,ak} be a set of relatively positive prime integers, a positive integer N is called representable byA if exists non-negatives integersx1,x2,...,xk, such thatN = P k=1 aixi. The Frobenius Problem consits in determining the largest integer, denoted with g(A), that is not representable by A. In this work we present an algorithm to solve the Frobenius Problem using Grobner Bases. In the Apendix we present the algorithms developed in this work, implemented in the computer system algebra MuPAD.