  We investigate pairing symmetry and a transition temperature in a
quasi-one-dimensional repulsive Hubbard model. We solve the Eliashberg equation
using the third-order perturbation expansion with respect to the on-site
repulsion $U$. We find that when the electron number density is shifted from
the half-filled, a transition into unconventional superconductivity is
expected. When one dimensionality is weak, a spin-singlet state is favorable.
By contrast, when one dimensionality is strong and electron number density is
far from the half-filled, a spin-triplet state is stabilized. Finally, we
discuss the possibility of unconventional superconductivity caused by the
on-site Coulomb repulsion in $\beta$-Na$_{0.33}$V$_2$O$_5$.
