We present a quantitative star formation history of the nearby dwarf galaxy UGCA 92. This irregular dwarf is situated in the vicinity of the Local Group of galaxies in a zone of strong Galactic extinction (IC 342 group of galaxies). The galaxy was resolved into stars, including the old red giant branch, with HST/ACS. We constructed a model of the resolved stellar populations and measured the star formation rate and metallicity as functions of time. The main star formation activity period occurred about 8–14 Gyr ago. These stars are mostly metal-poor, with a mean metallicity [Fe/H] ∼−1.5 to −2.0 dex. About 84 per cent of the total stellar mass was formed during this event. There are also indications of recent star formation starting about 1.5 Gyr ago and continuing to the present. The star formation in this event shows moderate enhancement from ∼200 to 300 Myr ago. It is very likely that the ongoing star formation period has a higher metallicity of about −0.6 to −0.3 dex. UGCA 92 is often considered to be the companion to the starburst galaxy NGC 1569. A comparison of our star formation history of UGCA 92 with that of NGC 1569 reveals no causal or temporal connection between recent star formation events in these two galaxies. We suggest that the starburst phenomenon in NGC 1569 is not related to the galaxy’s closest dwarf neighbours and does not affect their star formation history.