K2-18 b is a transiting mini-Neptune that orbits a nearby (38 pc), cool M3 dwarf and is located inside its region of temperate irradiation. We report on the search for hydrogen escape from the atmosphere K2-18 b using Lyman-α transit spectroscopy with the Space Telescope Imaging Spectrograph instrument installed on the Hubble Space Telescope. We analyzed the time-series of fluxes of the stellar Lyman-α emission of K2-18 in both its blue- and redshifted wings. We found that the average blueshifted emission of K2-18 decreases by 67% ± 18% during the transit of the planet compared to the pre-transit emission, tentatively indicating the presence of H atoms escaping vigorously and being blown away by radiation pressure. This interpretation is not definitive because it relies on one partial transit. Based on the reconstructed Lyman-α emission of K2-18, we estimate an EUV irradiation in the range 101 − 102 erg s−1 cm−2 and a total escape rate on the order of 108 g s−1. The inferred escape rate suggests that the planet will lose only a small fraction (< 1%) of its mass and retain its volatile-rich atmosphere during its lifetime. More observations are needed to rule out stellar variability effects, confirm the in-transit absorption, and better assess the atmospheric escape and high-energy environment of K2-18 b.