Л generalized projective implicitization theorem is presented that can be used to solve the implicitization of rational parametric curves and surfaces in an affinc space. The Groebner bases technique is used to implement the algorithm. The algorithm has the advantages that it can handle base points in a paraineliizaiioti, and no extra factors will be introduced into an implicit equation. The complexity of the algorithm in terms of the degrees of the polynomials in the Groebner basis is better than the existing method.