Addressing neonatal mortality is an important priority for improving the health and well-being of newborns. Almost two-thirds of infant deaths occur in the first month of life; among these, more than two-thirds die in their first week. Therefore, the aim of this study was to assess the mortality rate and predictors of mortality among neonates admitted to the neonatal intensive care unit (NICU) at Tikur Anbessa Specialized Hospital in Addis Ababa, Ethiopia, in 2023. An institutional-based retrospective follow-up study was conducted using 459 neonates who were admitted to the NICU at Tikur Anbessa Specialized Hospital from January 2020 to December 2022. The data were extracted from randomly selected charts using a pretested data extraction checklist. The Nelson Alan curve with log-rank test was used to compare the presence of differences in the mortality rate of different groups over different categorical variables. The cox proportional hazards analysis model was used to identify predictors of neonatal death. The presence and absence of statistical significance was considered at a p-value of less than 0.05 and the strength of association was measured using AHR. The neonatal mortality rate was 3.1 (95% CI: 1.3-4.9) per 1,000 neonate-days. Low birth weight (AHR = 1.44: 95% CI: 1.06-3.13), exclusive breast-feeding (AHR = 0.74: 95% CI: 0.35-0.95), and time of exclusive breast-feeding (AHR = 0.92: 95% CI: 0.49-0.99) were the identified predictors of newborn mortality. The neonatal mortality rate was high. Low birth weight of the neonate, exclusive breast-feeding initiation, and time of exclusive breast-feeding were independent predictors of neonatal death. Therefore, empowering mothers to exclusively breastfeed their children, which is a cost-effective, safe, and realistic option, can significantly minimize infant mortality.