  We perform a first principles band calculation for a group of
quasi-two-dimensional organic conductors \beta-(BDA-TTP)2MF6 (M=P, As, Sb, Ta).
The ab-initio calculation shows that the density of states (DOS) is correlated
with the band width of singly occupied (highest) molecular orbital (SOMO),
while it is not necessarily correlated with the unit cell volume. The direction
of the major axis of the cross section of the Fermi surface lies in the
\Gamma-B direction, which differs from that obtained by the extended Huckel
calculation. Then, we construct a tight-binding model which accurately
reproduces the ab-initio band structure. The obtained transfer energies give
smaller dimerization than in the extended Huckel band. As for the difference of
the anisotropy of the Fermi surface, the transfer energies along the
inter-stacking direction are smaller than those obtained in the extended Huckel
calculation. Assuming spin-fluctuation-mediated superconductivity, we apply
random phase approximation (RPA) to a two-band Hubbard model. This two-band
Hubbard model is composed of the tight-binding model derived from the first
principles band structure and an on-site (intra-molecule) repulsive interaction
taken as a variable parameter. The obtained superconducting gap changes sign
four times along the Fermi surface like in a d-wave gap, and the nodal
direction is different from that obtained in the extended Huckel model. Anion
dependence of Tc is qualitatively consistent with the experimental observation.
