Abstract The prompt phase of gamma-ray bursts (GRBs) contains essential information regarding their physical nature and central engine, which are as yet unknown. In this paper, we investigate the self-organized criticality phenomenon in GRB prompt phases as done in X-ray flares of GRBs. We obtain the differential and cumulative distributions of 243 short GRB pulses, such as peak flux, FWHM, rise time, decay time, and peak time in the fourth BATSE Time-Tagged Event Catalog with the Markov Chain Monte Carlo technique. It is found that these distributions can be well described by power-law models. In particular, comparisons are made with 182 short GRB pulses in the third Swift GRB Catalog from 2004 December to 2019 July. The results are essentially consistent with the BATSE ones. We notice that there is no obvious power-law index evolution across different energy bands for either BATSE or Swift short GRBs. The joint analysis suggests that the GRB prompt phase can be explained by a fractal-diffusive self-organized criticality system with the spatial dimension S = 3 and the classical diffusion β = 1. Our findings show that GRB prompt phases and X-ray flares possess the very same magnetically dominated stochastic process and mechanism.