  We study theoretically competition between the charge ordering and the
superconductivity in two-dimensional organic conductor
beta-(meso-DMBEDT-TTF)_2PF_6. We analyze the extended Hubbard model on a
weakly-dimerized lattice based on the random phase approximation and Eliashberg
equations. We found reentrant behavior of the checkerbord-type charge-ordered
phase in the phase diagram, and the triplet superconductivity due to the charge
fluctuation in the neighboring region. In the low temperature and high pressure
region, the singlet superconductivity also appears due to the enhancement of
the spin fluctuation.
