We present an algorithm to compute the Hilbert series of a homogeneous ideal in a polynomial ring. From an ideal I, generated by the principal monomials of a Grobner basis, we compute the Hilbert series \(Hilb_{k[x_1 ,...,x_n ]/I}\)(t)=T I (t)/(1−t) n . The polynomial T I is computed by recursively factoring out a monomial m of degree d at each step $$T_I (t) = T_{I + (m)} (t) + t^d T_{I + Ann(m)} (t).$$ .