Abstract Sub-damped Lyman α systems (subDLAs; H i column densities of 19.0 ≤ logN(H i) < 20.3) are rarely included in the cosmic H i census performed at redshifts zabs ≳ 1.5, yet are expected to contribute significantly to the overall H i mass budget of the Universe. In this paper, we present a blindly selected sample of 155 subDLAs found along 100 quasar sightlines (with a redshift path-length ΔX = 475) in the XQ-100 legacy survey to investigate the contribution of subDLAs to the H i mass density of the Universe. The impact of X-Shooter’s spectral resolution on Ly α absorber identification is evaluated, and found to be sufficient for reliably finding absorbers down to a column density of logN(H i) ≥ 18.9. We compared the implications of searching for subDLAs solely using H i absorption versus the use of metal lines to confirm the identification, and found that metal-selection techniques would have missed 75 subDLAs. Using a bootstrap Monte Carlo simulation, we computed the column density distribution function (f(N, X)) and the cosmological H i mass density ($Ω _{\rm H\,{\small I}}$) of subDLAs and compared with our previous work based on the XQ-100 damped Lyman α systems. We do not find any significant redshift evolution in f(N, X) or $Ω _{\rm H\,{\small I}}$ for subDLAs. However, subDLAs contribute 10–20 per cent of the total $Ω _{\rm H\,{\small I}}$ measured at redshifts 2 < z < 5, and thus have a small but significant contribution to the H i budget of the Universe.