Infant mortality is a major portion of under-five mortality as it is the least defended period of a child’s life. The objective of this study is to determine the most significant risk factors for neonatal and infant mortality in Bangladesh. Bangladesh demography and health survey (BDHS), 2014 dataset was taken to conduct this study. The dataset consisted of 4663 respondents. Neonatal and infant mortality was reported among 122 and 155 children respectively. To conduct the study, we used chi-square test to show the association between different selected potential risk factors along with neonatal and infant mortality. We also adopted logistic regression (LR) to determine the high risk factors of neonatal and infant mortality based on p-values, odds ratio (OR), including 95% confidence interval (CI). LR showed that Barisal division has the lowest odds for both neonatal (OR= 0.236; p<0.01) and infant (OR= 0.281; p<0.01) mortality. Fathers with no education showed highest odds of neonatal (OR= 3.040; p<0.01) and infant (OR= 2.867; p<0.01) death. Mothers with no education showed highest odds of infant mortality (OR= 2.850; p<0.05). Our finding helps the policy maker to take the necessary steps to address and controls the most significant risk factors to reduce neonatal and infant mortality.