We present a study of the HI gas content of a large K-band selected sample of 88 close major-merger pairs of galaxies (H-KPAIR) which were observed by $it Herschel$. We obtained the 21 cm HI fine-structure emission line data for a total of 70 pairs from this sample, by observing 58 pairs using the Green Bank Telescope (GBT) and retrieving the HI data for an addition 12 pairs from the literature. In this HI sample, 34 pairs are spiral-spiral (S+S) pairs, and 36 are spiral-elliptical (S+E). Based on these data, we studied the HI-to-stellar mass ratio, the HI gas fraction and the HI star formation efficiency (SFE$_{mathrm{HI}}$ = star formation rate/$M_{mathrm{HI}}$) and searched for differences between S+S and S+E pairs, as well as between pairs with and without signs for merger/interaction. Our results showed that the mean HI-to-stellar mass ratio of spirals in these pairs is $=7.6pm1.0 %$, consistent with the average HI gas fraction of spiral galaxies in general. The differences in the HI gas fraction between spirals in S+S and in S+E pairs, and between spirals in pairs with and without signs of merger/interaction are insignificant ($< 1 sigma$). On the other hand, the mean SFE$_{mathrm{HI}}$ of S+S pairs is $sim4.6times$ higher than that of S+E pairs. This difference is very significant ($sim 4sigma$) and is the main result of our study. There is no significant difference in the mean SFE$_{mathrm{HI}}$ between galaxies with and without signs of merger/interaction. The mean SFE$_{mathrm{HI}}$ of the whole pair sample is $10^{-9.55pm 0.09} mathrm{yr}^{-1}$, corresponding to a HI consumption time of $3.5pm0.7$ Gyrs.
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