We investigate whether the correlation between the hard X-ray photon index ({Gamma}) and accretion rate for super-Eddington accreting quasars is different from that for sub-Eddington accreting quasars. We construct a sample of 113 bright quasars from the Sloan Digital Sky Survey Data Release 14 quasar catalog, with 38 quasars as the super-Eddington subsample and 75 quasars as the sub-Eddington subsample. We derive black hole masses using a simple-epoch virial mass formula based on the H{beta} lines, and we use the standard thin disk model to derive the dimensionless accretion rates (M) for our sample. The X-ray data for these quasars are collected from the Chandra and XMM-Newton archives. We fit the hard X-ray spectra using a single power-law model to obtain {Gamma} values. We find a statistically significant (R_S_=0.43, p=7.75x10^-3^) correlation between {Gamma} and M for the super-Eddington subsample. The {Gamma}-M correlation for the sub-Eddington subsample is also significant, but weaker (R_S_=0.30, p=9.98x10^-3^). Linear regression analysis shows that {Gamma}=(0.34{+/-}0.11)log(M)+(1.71{+/-}0.17) and {Gamma}=(0.09{+/-}0.04)log(M)+(1.93{+/-}0.04) for the super- and sub-Eddington subsamples, respectively. The {Gamma}-M correlations of the two subsamples are different, suggesting different disk-corona connections in these two types of systems. We propose one qualitative explanation of the steeper {Gamma}-M correlation in the super-Eddington regime that involves larger seed photon fluxes received by the compact coronae from the thick disks in super-Eddington accreting quasars.