The deterioration or death of a person might be due to a variety of physical factors. It is challenging, if not impossible, to identify and precisely account for all of these physical factors. As a result, selecting a theoretical model to represent survival neutrosophic data is an art and a science. This study presents the neutrosophic structure of the Weibull model that has been frequently used to represent survival data. Mathematical characteristics of the neutrosophic Weibull distribution under neutrosophic statistics are developed. The approach of maximum likelihood is established for estimating the neutrosophic distributional parameters. Additionally, a simulation experiment is carried out to evaluate the performance of distributional parameters. The application of the proposed model is also provided in terms of a real dataset.