  We study the pairing symmetry and the topological properties of the
hydrogen-doped ACr$_3$As$_3$ superconductors. Based on our first-principle band
structure with spin-orbit-coupling (SOC), we construct tight binding model
including the on-site SOC terms, equipped with the multi-orbital Hubbard
interactions. Then using the random-phase-approximation (RPA) approach, we
calculate the pairing phase diagram of this model. Our RPA results yield the
triplet pz-wave pairing in the
($\left(\uparrow\downarrow+\downarrow\uparrow\right)$) spin channel to be the
leading pairing symmetry all over the experiment relevant hydrogen-doping
regimes. This pairing state belongs to the spin-U(1)-symmetry protected
time-reversal-invariant topological nodal-line superconductivity. Determined by
the momentum-dependent topological invariant Z (kx; ky), the whole (001)
surface Brillouin zone is covered with topological flat bands with different
regimes covered with different numbers of flat surface bands, which can be
detected by the scanning tunneling microscope experiments.
