Luminous starbursts are observed to occur mostly as a result of a collision/merger in gas-rich galaxies, and most luminous infrared galaxies (LIGs) are indeed gas-rich mergers. In order to determine the relationship between the IR and molecular gas properties and the galaxy-galaxy interactions, we study LIG mergers in the intermediate merging process. We have observed nearly 20 LIG mergers and together with the CO data in the literature, we have found a correlation between the CO luminosity, LCO, and the projected separation of merger nuclei, RSep, in > 50 LIG mergers. The correlation suggests the molecular content is decreasing as merging advances and is better established with ~ 40 LIG mergers excluding ultraluminous ones, which resembles more a volume-limited, statistically complete sample of LIG mergers. In addition, an anti-correlation between LIR/LCO (the measure of star formation efficiency, SFE) and RSep is evident. One interpretation is that the molecular gas content of LIG mergers is being rapidly depleted due to the merger-induced starbursts and the increase of SFE as merging progresses.