Due to a disparity in Human Development Index (HDI) among regencies and cities in Special Region of Yogyakarta, this study aimed to examine whether HDI convergence occurred in this province. The data were sourced from the Statistics of Special Region of Yogyakarta, including HDI, infrastructure, and gross regional domestic product in four regencies and one city from 2001 to 2019. The infrastructure consists of installed electricity, education, and health facilities. The results showed an absence of HDI convergence between regions in the Special Region of Yogyakarta. Furthermore, HDI growth in the impoverished region was slower than in leading ones, resulting in a gap. The infrastructure gap made the impoverished region unable to catch up with leading ones, causing an HDI divergence. In contrast, Gross Regional Domestic Product (GRDP) has no impact on HDI. Therefore, the government needs to improve infrastructure in disadvantaged areas to increase HDI.