The electronic structures of 13-atom Ru clusters with three possible high-symmetry geometries have been studied using the discrete-variational local-spin-density-functional method. The results indicata that all clusters with different symmetry at their equilibrium configuration have two magnetie solutions, and the low-spin solutions of the clusters are energetically more stable than the high-spin solutions of the clusters for each kind of symmetry. The ground state is the ＩhRu13 cluster, and has the magnetic moment of ４μB, or ０.３１μB per atom, which is in good agreement with the upper limit of experimental observation, ０.２９μB per atom. The reason for the contradiction of the magnetic moments between previous theory and experiment is that multiple magnetic solutions exist for the Kohn-Sham equations. The calculated results are compared and discussed with those of the previous theory. The real geometry of the Ru13 cluster is suggested to be a distorted icosahedron.