Abstract Background Programmatic and research agendas surrounding neonatal mortality are important to help countries attain the child health related 2030 Sustainable Development Goal (SDG). In Burundi, the Neonatal Mortality Rate (NMR) is 25 per 1000 live births. However, high quality evidence on the over time evolution of inequality in NMR is lacking. This study aims to address the knowledge gap by systematically and comprehensively investigating inequalities in NMR in Burundi with the intent to help the country attain SDG 3.2 which aims to reduce neonatal mortality to at least as low as 12 per 1000 live births by 2030. Methods The Burundi Demographic and Health Survey (BDHS) data for the periods of 2010 and 2016 were used for the analyses. The analyses were carried out using the WHO’s HEAT version 3.1 software. Five equity stratifiers: economic status, education, residence, sex and subnational region were used as benchmark for measuring NMR inequality with time over 6 years. To understand inequalities from a broader perspective, absolute and relative inequality measures, namely Difference, Population Attributable Risk (PAR), Ratio, and Population Attributable Fraction (PAF) were calculated. Statistical significance was measured by computing corresponding 95% Confidence Intervals (CIs). Results NMR in Burundi in 2010 and 2016 were 36.7 and 25.0 deaths per 1000 live births, respectively. We recorded large wealth-driven (PAR = -3.99, 95% CI; − 5.11, − 2.87, PAF = -15.95, 95% CI; − 20.42, − 11.48), education related (PAF = -6.64, 95% CI; − 13.27, − 0.02), sex based (PAR = -1.74, 95% CI; − 2.27, − 1.21, PAF = -6.97, 95% CI; − 9.09, − 4.86), urban-rural (D = 15.44, 95% CI; 7.59, 23.29, PAF = -38.78, 95% CI; − 45.24, − 32.32) and regional (PAR = -12.60, 95% CI; − 14.30, − 10.90, R = 3.05, 95% CI; 1.30, 4.80) disparity in NMR in both survey years, except that urban-rural disparity was not detected in 2016. We found both absolute and relative inequalities and significant reduction in these inequalities over time - except at the regional level, where the disparity remained constant during the study period. Conclusion Large survival advantage remains to neonates of women who are rich, educated, residents of urban areas and some regions. Females had higher chance of surviving their 28th birthday than male neonates. More extensive work is required to battle the NMR gap between different subgroups in the country.