The current–voltage (I–V) characteristics of a doped weakly coupled GaAs/AlAs superlattice (SL) with narrow barriers are measured under hydrostatic pressure from 1 bar to 13.5 kbar at both 77 and 300 K. The experimental results show that, contrary to the results in SL with wide barriers, the plateau in the I–V curve at 77 K does not shrink with increasing pressure, and becomes wider after 10.5 kbar. It is explained by the fact that the EΓ1–EΓ1 resonance peak is higher than the EΓ1–EX1 resonance peak. At 300 K, however, because of the more important contribution of the nonresonant component to the current, the plateau shrinks with increasing pressure.