The design of stable electrolyte materials with high proton conductivity for use in proton exchange membrane fuel cells remains a challenge. Most of the materials explored have good conductivity at high relative humidity (RH), but significantly decreased conductivity at reduced RH. Here we report a chemically stable and structurally flexible metal–organic framework (MOF), BUT-8(Cr)A, possessing a three-dimensional framework structure with one-dimensional channels, in which high-density sulfonic acid (–SO3H) sites arrange on channel surfaces for proton conduction. We propose that its flexible nature, together with its –SO3H sites, could allow BUT-8(Cr)A to self-adapt its framework under different humid environments to ensure smooth proton conduction pathways mediated by water molecules. Relative to other MOFs, BUT-8(Cr)A not only has a high proton conductivity of 1.27 × 10−1 S cm−1 at 100% RH and 80 °C but also maintains moderately high proton conductivity at a wide range of RH and temperature.