  Comparing to the inactive and gas-poor normal lenticular galaxies (S0s) in
the local universe, we study a barred star-forming S0 galaxy, PGC 34107, which
has been observed by the Centro Astron\'{o}mico Hispano Alem\'{a}n (CAHA) 3.5-m
telescope and the Northern Extended Millimeter Array (NOEMA). The spatially
resolved ionized gas and molecular gas traced by $^{12}$CO(1-0), hereafter
CO(1-0), show the similar distribution and kinematics to the stellar component
with an off-center star-forming region, $\sim$380 pc away from the center. The
resolved kinematics of molecular CO(1-0) emission reveals that there is a
blueshifted (redshifted) velocity component on the receding (approaching) side
of the galaxy along the stellar bar. This might provide a plausible evidence of
non-circular motion, such as the bar-induced molecular gas inflow. The velocity
of molecular gas inflow decreases with approaching towards the peak of the
off-center star formation in the north, which might be associated with the
inner Lindblad resonance (ILR). In addition to CO(1-0), we also detect the
isotopic line of $^{13}$CO(1-0). Most $\rm H\alpha$, CO(1-0) and $^{13}$CO(1-0)
emissions are concentrated on this northern star-forming region. We find that
PGC 34107 follows the local stellar mass-metallicity relation, star-forming
main sequence, and the Kennicutt-Schmidt law. The resolved and integrated
molecular gas main sequence suggest that there is a higher gas fraction in the
galaxy central region, which supports a scenario that the bar-induced gas
reservoir provides the raw material, and subsequently triggers the central star
formation.
