The variability in multi-pulse gamma-ray bursts (GRBs) may help to reveal the mechanism of underlying processes from the central engine. To investigate whether the self-organized criticality (SOC) phenomena exist in the prompt phase of GRBs, we statistically study the properties of GRBs with more than 3 pulses in each burst by fitting the distributions of several observed physical variables with a Markov Chain Monte Carlo approach, including the isotropic energy $E_{rm iso}$, the duration time $T$ and the peak count rate $P$ of each pulse. Our sample consists of 454 pulses in 93 GRBs observed by the CGRO/BATSE satellite. The best-fitting values and uncertainties for these power-law indices of the differential frequency distributions are: $alpha^d_{E}=1.54 pm 0.09$, $alpha^d_{T}=1.82_{-0.15}^{+0.14}$ and $alpha^d_{P}=2.09_{-0.19}^{+0.18}$, while the power-law indices in the cumulative frequency distributions are: $alpha^c_{E}=1.44_{-0.10}^{+0.08}$, $alpha^c_{T}=1.75_{-0.13}^{+0.11}$ and $alpha^c_{P}=1.99_{-0.19}^{+0.16}$. We find that these distributions are roughly consistent with the physical framework of a Fractal-Diffusive, Self-Organized Criticality (FD-SOC) system with the spatial dimension $S=3$ and the classical diffusion $beta$=1. Our results support that the jet responsible for the GRBs should be magnetically dominated and magnetic instabilities (e.g., kink model, or tearing-model instability) lead the GRB emission region into the SOC state.
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