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Abstract Objective: To examine the height-for-age z-score (HAZ) of 0–35 months’ children along with stunting prevalence to identify trends, changes and available nutrition-sensitive and specific determinants that could help explain the long-term variation in child linear growth using successive Bangladesh Demographic and Health Surveys (BDHS) data from 1996 to 2018. Design: The BDHS pooled data are used for determining the key outcome variables HAZ, stunting and severe stunting. Trends, kernel-weighted local polynomial smoothing illustrations, pooled multivariable linear probability model (LPM), ordinary least squares method (OLS) and regression decomposition were used. Participants: Mothers having 0–35 months’ children, the most critical age range for growth faltering. Results: The mean HAZ increased by 0·91(±1·53) with 0·041 annual average change, while the percentages of stunting (–26·63 ± 0·54) and severe stunting (–21·12 ± 0·48) showed a reduction with 1·21 and 0·96 average annual changes, respectively. The average HAZ improvement (0·42 ± 1·56) in urban areas was less than the rural areas (1·16 ± 1·44). Similar patterns followed for stunting and severe stunting. The prenatal doctor visits (3064·65 %), birth in a medical facility (1054·32 %), breastfeeding initiation (153·18 %) and asset index (144·73 %) demonstrated a huge change. The findings of OLS, LPM and regression decomposition identified asset index, birth order, paternal and maternal education, bottle-fed, prenatal doctor visit, birth in a medical facility, vaccination, maternal BMI and ever-breastfed as influencing factors to predict the long-term changes of stunting and severe stunting. Conclusion: The nutrition-sensitive and specific factors identified through regression decomposition describing long-term variation in child linear growth should be focused further to attain the sustainable development goals.