  We investigate the pairing symmetry of the newly synthesized
quasi-one-dimension K$_2$Cr$_3$As$_3$ superconductor based on the six-band
model. We adopt standard random-phase-approximation to study the Hubbard-Hund
model of the system. Our results confirm the conclusions obtained from our
previous three-band model: the triplet $p_z$ and $f_{y^3-3x^2y}$ wave pairings
serve as the leading pairing symmetries in the weak and strong Hund's rule
coupling regimes, respectively. For physically realistic parameters, the
triplet $p_z$-wave pairing driven by ferromagnetic fluctuations is the leading
pairing symmetry of the system. The consistency between the results of these
two models suggests that the obtained $p_z$-wave pairing symmetry is physical
and model-independent.
