We present ab-initio calculations for the electronic structure and supercon
ducting properties of YBa2Cu3O7 (YBCO). The electronic structure was calcul
ated using a self-consistent ab-initio LCAO method. We solved the anisotrop
ic Eliashberg gap equation numerically. The strong coupling of the high ene
rgy optical phonons around 60 - 73 meV, with the electrons at the Fermi sur
face, leads to a high T-c in YBCO. The calculated T-c is about 89 K for mu*
= 0.1. The good agreement of the calculated results with experimental meas
urements and the ab-initio nature of the calculations support the scenario
of an anisotropic s-wave superconductor for YBCO.