Estimating cure-rate is a popular research topic in the study of immunity of individuals against terminal diseases such as cancers and HIV. In the literature, mainly estimation based on parametric models have been studied so far, with a few exceptions. In this paper, we use the Poisson smoothing idea of Chaubey and Sen (1996) to propose two novel non-parametric estimators under Case-1 interval censoring, which improve upon previously proposed ones (Sen and Tan, 2008). We show that our estimators are consistent. In addition, their asymptotic normality is studied, and we apply our estimator to estimate cure-rate on data collected for lung tumor in mice (Finkelstein
and Wolfe, 1985). Finally, the smoothing parameter for optimum estimation has been determined by using Jackknife method.