The early initiation of breast-feeding (EIBF) within 1 h of birth, exclusive breast-feeding (EBF) to 6 months and continued breast-feeding (CBF) to 2 years are key infant and young child feeding guidelines promoted globally for optimal child health and development. Using publicly available national survey data from the five most recent, consecutive Bangladesh Demographic and Health Surveys (2004, 2007, 2011, 2014 and 2017–2018), we assessed the trends in these key breast-feeding indicators. Multiple multilevel logistic regression models were built to assess socio-demographic predictors of breast-feeding using the latest 2017–2018 data set. Both EIBF and EBF have increased significantly between 2004 and 2017–2018, from 26 % to 60 % and 36 % to 68 %, respectively, and CBF decreased from 94 % to 85 %. Caesarean section delivery conferred lower EIBF practice (OR = 0·34, 95 % CI 0·27, 0·42) compared with vaginal delivery. Women who were currently working had 32 % lower odds of EBF (OR = 0·68, 95 % CI 0·48, 0·95). Compared with delivery at home, women who delivered in a health facility had 81 % higher odds of EBF (OR = 1·81, 95 % CI 1·25, 2·34). Larger family size (≥5) also predicted EBF (OR = 1·70, 95 % CI 1·21, 2·40). Rural residency was associated with 2·39 (95 % CI 1·32, 4·31) times of higher odds of CBF. Regional variation was also predictive of the various breast-feeding indicators. Although Bangladesh currently exceeds the 2019 global prevalence rates for these three breast-feeding indicators, efforts should be made to continue improving EIBF and EBF and to prevent future decreases in CBF.