Neonatal death is often referred to maternal complications during pregnancy, and other exogenous factors that exist around the time of birth or shortly after birth. The United Nations Sustainable Development Goals (UNSDG)-Goal 3, Targets 3.2 aimed at ending preventable deaths of newborns by demanding that all countries should reduce neonatal mortality to 12 per 1000 live births by 2030. The objective of the study was to examine the relationship between mothers’ socio-economic and demographic factors on neonatal deaths in Nigeria. The study used quantitative data from the 2013 Nigeria Demographic and Health Surveys (NDHS). The data analyzed consisted of 26,826 women aged 15–49 years who had a live or dead birth within the 5 years preceding the survey. STATA 12 computer software was used to carry out data analyses. Data analyses were at univariate (frequency distribution), bivariate (chi-square) and due to the dichotomous nature of the outcome variable (i.e., whether a child was born alive or dead during the delivery; coded as (1, 0), a binary logistic regression was carried out to examine the relationships between various socio-demographic factors, antenatal clinic attendance and neonatal mortality in Nigeria. The results, among others, revealed that background factors of the women such as age, region, residence, education, and wealth status have a significant association with neonatal mortality (P < 0.05). The study also found that adequate antenatal clinic attendance helps to reduce neonatal deaths. The study recommended that women should be encouraged to observe regular antenatal clinic visits during pregnancy and also go for institutional delivery for possible reduction of neonates and infant deaths in Nigeria.