  We investigate the spin-triplet superconductivity mediated by phonons in
quasi-one-dimensional (Q1D) systems with open Fermi surfaces. We obtain the
ground state phase diagrams. It is found that spin-triplet superconductivity
occurs for weak screening and strong on-site Coulomb interaction, even in the
absence of any additional nonphonon pairing interactions. We find that the
nodeless spin-triplet state is more favorable than the spin-triplet state with
line nodes, for the parameter values of the Q1D superconductors (TMTSF)_2X. We
also find that Q1D open Fermi surface, which is the specific feature of this
system, plays an essential role in the pairing symmetry. We discuss the
compatibility of the present results with the experimental results in these
compounds.
