  The Seebeck coefficient is examined for two-dimensional Dirac electrons in
the three-quarter filled organic conductor alpha-(BEDT-TTF)_2I_3 under
hydrostatic pressure, where the Seebeck coefficient is proportional to the
ratio of the thermoelectric conductivity to the electrical conductivity. We
present an improved tight-binding model in two dimensions with transfer
energies determined from first-principles density functional theory
calculations with an experimentally determined crystal structure. The
temperatutre dependence of the Seebeck coefficient is calculated by adding
impurity and electron-phonon scatterings. Noting a zero-gap state due to the
Dirac cone, which results in a competition from contributions between the
conduction and valence bands, we show positive S_x and S_y at finite
temperatures and analyze them in terms of spectral conductivity. The relevance
of the calculated S_x (perpendicular to the molecular stacking axis) to the
experiment is discussed.
