Abstract The number of long-duration gamma-ray burst (LGRB) host galaxies with measured metallicities and host masses has expanded sufficiently to investigate how the distributions of these properties change with redshift. Using the combined host galaxy metallicity sample from Graham & Fruchter and Krühler et al., we find a surprising lack of evolution in the LGRB metallicity distribution across different redshifts. In particular, the fraction of LGRB hosts with relatively high metallicity (12+log(O/H) ≥ 8.4) remains essentially constant out to z = 2.5. This result is at odds with the evolution in the mass–metallicity relation of typical galaxies, which become progressively more metal poor with increasing redshift. A similar result is found when converting the LGRB host galaxy mass distribution taken from the Swift GRB Host Galaxy Legacy Survey (SHOALS) sample to a corresponding metallicity distribution by applying a redshift-dependent mass–metallicity relation. The SHOALS sample is compiled using an unbiased selection function implying that the observed lack of evolution in the host galaxy high-metallicity distribution is not caused by selection effects. However, the LGRB host galaxy metallicities estimated from the stellar mass are typically a quarter dex higher at all redshifts than the metallicity we measure spectroscopically. This implies that using mass–metallicity relationships to estimate host metallicities will thus produce a substantial systematic bias.