Final states containing baryons are kinematically accessible to weakly decaying $B$ mesons. The measurement of the exclusive branching fractions of baryonic $B$ decays, as well as studies on the dynamic of the decay, may allow better understanding of baryon production in $B$ decays and, more generally, hadron fragmentation into baryons. We present here a search for the decay $B \to p p \bar{p} \bar{p}$, not yet observed, by using a data set consisting of about 470 million $B\bar{B}$ pairs collected with the BaBar detector at the SLAC National Accelerator Laboratory. We select $11.1\pm 4.6$ candidate events, corresponding to a signal significance of $2.9 \sigma$, and obtain the branching fraction of $(1.14\pm0.47_{\mathrm{(stat)}}\pm 0.17_{\mathrm{(syst)}})\times 10^{-7}$.