ABSTRACT We present morphological analyses of post-starburst galaxies (PSBs) at 0.7 < z < 0.9 in the COSMOS field. We fitted ultraviolet to mid-infrared multiband photometry of objects with i < 24 from COSMOS2020 catalogue with population synthesis models assuming non-parametric, piece-wise constant function of star formation history, and selected 94 of those galaxies that have high specific star formation rates (SSFRs) of more than 10−9.5 yr−1 in 321–1000 Myr before observation and an order-of-magnitude lower SSFRs within recent 321 Myr. We devised a new non-parametric morphological index which quantifies concentration of asymmetric features, CA, and measured it as well as concentration C and asymmetry A on the Hubble Space Telescope/Advanced Camera for Surveys IF814W-band images. While relatively high C and low A values of PSBs are similar to those of quiescent galaxies rather than star-forming galaxies, we found that PSBs show systematically higher values of CA than both quiescent and star-forming galaxies; 36 per cent of PSBs have log CA > 0.8, while only 16 per cent (2 per cent) of quiescent (star-forming) galaxies show such high CA values. Those PSBs with high CA have relatively low overall asymmetry of A ∼ 0.1, but show remarkable asymmetric features near the centre. The fraction of those PSBs with high CA increases with increasing SSFR in 321–1000 Myr before observation rather than residual ongoing star formation. These results and their high surface stellar mass densities suggest that those galaxies experienced a nuclear starburst in the recent past, and processes that cause such starbursts could lead to the quenching of star formation through rapid gas consumption, supernova/active galactic nucleus feedback, and so on.