  The experimental observable properties of the triplet $p_z$-wave pairing
state, proposed by Wu {\em et al.} [arXiv:1503.06707] in quasi-one dimensional
A$_2$Cr$_3$As$_3$ materials, are theoretically investigated. This pairing state
is characterized by the line nodes on the $k_z=0$ plane on the Fermi surfaces.
Based on the three-band tight binding model, we obtain the specific heat,
superfluid density, Knight shift and spin relaxation rate and find that all
these properties at low temperature ($T\ll T_c$) show powerlaw behaviors and
are consistent available experiments. Particularly, the superfluid density
determined by the $p_z$-wave pairing state in this quasi-one dimensional system
is anisotropic: the in-plane superfluid density varies as
$\Delta\rho_{\parallel}\sim T$ but the out-plane one varies as
$\Delta\rho_{\perp}\sim T^3$ at low temperature. The anisotropic upper critical
field reported in experiment is consistent with the $S_z=0$ (i.e.,
$(\uparrow\downarrow+\downarrow\uparrow)$) $p_z$-wave pairing state. We also
suggest the phase-sensitive dc-SQUID measurements to pin down the triplet
$p_z$-wave pairing state.
