A growing corpus of evidence reveals that smoking patterns of migrant women tend to converge with that of the host population over time (‘acculturation paradox’). In this paper we aim to adopt a health equity perspective by studying the extent to which this pattern reflects a convergence with the group of natives who are more socioeconomically disadvantaged. Using population-based registers, we study 1,194,296 women who gave birth in Sweden between 1991 and 2012. Using logistic regression, we estimated odds ratios to assess the effect of duration of residence on the association between smoking during pregnancy and women's origin (classified according to inequality-adjusted Human Development Index (iHDI) of the country of birth). Sibling information and multilevel models were used to assess the extent to which our results might be affected by the cross-sectional nature of the data. Smoking during pregnancy increases with duration of residence among migrants from all levels of iHDI to such an extent that they tend to converge or increase in relation to the levels of the Swedish population with low education and low income, leaving behind the native population with high education and income. The results are robust to possible selection bias related to the cross-sectional nature of the data. Ourfindings indicate the need of a health equity perspective and suggest the use of ‘unequal assimilation’ rather than ‘acculturation paradox’ as a more suitable framework to interpret these findings.