Electronic structures of Pt-13 clusters and those adsorbed with hydrogen atoms based on the first principles calculations are studied for Pt-13 clusters of icosahedral (I-h) symmetry, cuboctahedral (O-h) symmetry and the systems of 8,12,14,20 hydrogen atoms adsorbing to them. Calculations have been done by the self-consistent local density functional scheme using the norm-conserving pseudopotential in the linear combination of the atomic orbital method. The equilibrium distances of Pt-Pt and Pt-H are calculated. The electronic structures of H adsorbed on Pt clusters are turned out to be the shell structure of "the giant atom." H-ls electrons fill n = 1 shell of Pt13H cluster with Pt-6s electrons. The energy levels of shell-2d of naked Pt-13 clusters and shell-n = 3,4 states of H adsorbed Pt-13 clusters, which come from H-ls antibonding are compared with experimental results of in situ x-ray absorption near-edge structure (XANES).