  We propose an extended Hubbard model with three molecular orbitals on a
hexagonal lattice with $D_{3h}$ symmetry to study recently discovered
superconductivity in A$_2$Cr$_3$As$_3$ (A=K,Rb,Cs). Effective pairing
interactions from paramagnon fluctuations are derived within the random phase
approximation, and are found to be most attractive in spin triplet channels. At
small Hubbard $U$ and moderate Hund's coupling, the pairing arises from
3-dimensional (3D) $\gamma$ band and has a spatial symmetry
$f_{y(3x^{2}-y^{2})}$, which gives line nodes in the gap function. At large
$U$, a fully gapped $p$-wave state, $p_{z}\hat{z}$ dominates at the quasi-1D
$\alpha $-band.
