Using a full-potential linear-muffin-tin-orbital molecular-dynamics (FP-LMTO-MD) method, we have performed calculations on the structures and the binding energies of Si₆₀ and Ge₆₀ clusters. The results calculated suggest that the stable structures for Si₆₀ and Ge₆₀ clusters are both distorted truncated icosahedra, with T_h symmetry. Their fullerene cage structures remain, but they look like puckered balls. Four distinct Si-Si bond lengths in Si₆₀, three distinct Ge-Ge bond lengths in Ge₆₀, and lower T_h symmetry make the two structures different from that with I_h symmetry and two C-C bond lengths in C₆₀.