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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 Astronómico Hispano Alemán (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 $\rm Hα$, 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.