Early initiation of breastfeeding (EIBF) is an essential practice for child health as well as for maternal health. This study aims to determine trends, prevalence, and factors associated with EIBF in Bangladesh. Data for this study were extracted from Bangladesh demographic and health surveys (BDHS) 2004, 2007, 2011, and 2014. This study found an increasing trend in EIBF in Bangladesh irrespective of the different characteristics of mothers and children. Chi-square test was conducted to find the association between EIBF and different factors. Multilevel logistic regression analysis was used to consider the hierarchical structure of the data. Regression result showed that educated parents [Adjusted odds ratio (AOR) = 1.14, 95% Confidence Interval (CI) = 1.04, 1.26 ], exposure to media [AOR = 1.13, CI = 1.05, 1.21], 2nd or 3rd birth order [AOR = 1.13, CI = 1.04, 1.23], wanted child [AOR = 1.12, CI = 1.02, 1.23], antenatal visit [AOR = 1.07, CI = 1.00, 1.15], antenatal visit by medically trained provider [AOR = 1.06, CI = 1.00,1.13] and rich wealth index [AOR = 1.10, CI = 1.01, 1.20] were positively associated with EIBF. In contrast, mothers with caesarian delivery [AOR = 0.36, CI = 0.31, 0.40], delivery in private facility [AOR = 0.83, CI = 0.73, 0.95], multiple birth, and higher maternal age were less likely to EIBF.