The geometric and magnetic properties of M-13 and M-13-doped Au-20 (M = Fe, Ti) clusters have been studied using the generalized gradient approximation based on the density functional theory. The optimized geometries of the clusters are close to the I-h structure within 0.006-0.05 nm tolerance. The lowest-energy spin states of the Fe-13 and Fe-13-doped Au-20 clusters are 44 mu(B) and 38 mu(B), respectively, while there is week ferromagnetic interaction between the Fe and Au atoms for the Fe-13-doped Au-20 cluster. On the other hand, the lowest energy spin states of the Ti-13 and Ti-13-doped Au-20 clusters are 6 mu(B) and 4 mu(B), respectively. The magnetic ordering is in a week ferromagnetic arrangement between the 12 surface Ti atoms and Au atoms, while in a week antiferromagnetic arrangement between the 12 surface Ti atoms and the core Ti atom. Comparing with the bare Fe-13 and Ti-13 clusters, the magnetic moments of Fe-13 and Ti-13 in Fe-13-doped Au-20 and Ti-13-doped Au-20 clusters are reduced by 6.81 mu(B) and 2.88 mu(B), respectively.