In this paper, a new distribution with four parameters named discrete exponentiated modified Topp-Leone Chen distribution is introduced, using the general approach of discretization. The discrete exponentiated modified Topp-Leone Chen distribution can be applied to model reliability and survival data in various fields. Some statistical properties including quantile, mean residual life, mean time to failure, mean time between failure, availability, Re ́nyi entropy, moments and order statistics are obtained. Maximum likelihood approach is applied under Type-II censored sample for estimating the unknown parameters of the discrete exponentiated modified Topp-Leone Chen distribution. Also, maximum likelihood estimators of the survival, hazard rate and alternative hazard rate functions are obtained. The confidence intervals for the parameters, survival, hazard rate and alternative hazard rate functions are obtained. A simulation study is carried out to illustrate the theoretical results of the maximum likelihood estimation. Finally, two real data sets are applied to illustrate the flexibility and applicability of the proposed model for real-life applications.