Modeling fractional data in various real life scenarios is a challenging task. This paper considers situations where fractional data are observed in the interval [0,1]. The unit-Lindley distribution has been discussed in the literature where its support lies between 0 and 1. In this paper, we focus on an inflated variant of the unit-Lindley distribution, where the inflation occurs at both 0 and 1. Various properties of the inflated unit-Lindley distribution are discussed and examined, including point estimation based on the maximum likelihood method and interval estimation. Finally, extensive Monte Carlo simulation and real-data analyses are carried out to compare the fit of our proposed distribution along with some of the existing ones such as the inflated beta and the inflated Kumaraswamy distributions.