First-principles molecular dynamics simulations have been employed to analyse the proton diffusion in cubic BaZrO3 perovskite at 1300 K. A non-linear effect on the proton diffusion coefficient arising from an applied isometric strain up to 2 % of the lattice parameter, and an evident enhancement of proton diffusion under compressive conditions have been observed. The structural and electronic properties of BaZrO3 are analysed from Density Functional Theory calculations, and after an analysis of the electronic structure, we provide a possible explanation for an enhanced ionic conductivity of this bulk structure that can be caused by the formation of a preferential path for proton diffusion under compressive strain conditions. By means of Nudged Elastic Band calculations, diffusion barriers were also computed with results supporting our conclusions.