Abstract Background To promote institutional delivery, the Government of India, through the Janani Suraksha Yojana (JSY) program, gives monetary reward to all pregnant women who give birth at the government or private health center. Despite providing cash assistance, a higher number of women are still preferring delivering at home. Therefore, this study sought to determine the prevalence of home births and identifying the factors influencing women’s choice of home deliveries. Methods Data from the National Family Health Survey (NFHS) conducted during 2005–06 and 2015–16 were used in the study. The respondents were women 15–49 years; a sample of 36,850 and 190,898 women in 2005–06 and 2015–16 respectively were included in the study. Multivariate logistic regression was used to determine the factors influencing home delivery. Income-related inequality in home delivery was quantified by the concentration index (CI) and the concentration curve (CC), and decomposition analysis was used to examine the inequality in the prevalence of home deliveries. Results The prevalence of home deliveries has reduced from 58.5% in 2005–06 to 18.9% in 2015–16. The odds of delivering babies at home were lower among women who had full ANC in 2005–06 [AOR: 0.34; CI: 0.28–0.41] and in 2015–16 [AOR: 0.41; CI: 0.38–0.45] and were higher among women with four or higher parity in 2005–06 [AOR: 1.70; CI: 1.49–1.92] and in 2015–19 [AOR: 2.16; CI: 2.03–2.30]. Furthermore, the odds of delivering babies at home were higher among rural women and were lower among women with higher education. It was found that the value of CI increased from − 0.25 to − 0.39 from 2005-06 to 2015–16; this depicts that women delivering babies at home got more concentrated among women from lower socio-economic status. Conclusion There is a need to promote institutional deliveries, particular focus to be given to poor women, women with higher parity, uneducated women, and rural women. ANC is the most concurring contact point for mothers to get relevant information about the risks and complications they may encounter during delivery. Therefore, effort should be directed to provide full ANC. Targeted interventions are called for to bring improvements in rural areas.