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Sorted by the photon fluences of short Gamma-ray Bursts (SGRBs) detected by the Fermi-Gamma Ray Burst Monitor (GBM), nine brightest bursts are selected to perform a comprehensive analysis. All GRB lightcurves are fitted well by 1 to 3 pulses that are modelled by fast-rising exponential decay profile (FRED), within which the resultant rising time is strongly positive-correlated with the full time width at half maxima (FWHM). A photon spectral model involving a cutoff power-law function and a standard blackbody function (CPL + BB) could reproduce the spectral energy distributions of these SGRBs well in the bursting phase. The CPL’s peak energy is found strongly positive-correlated with the BB’s temperature, which indicates they might be from the same physical origin. Possible physical origins are discussed to account for these correlations.