In practical scenarios, it is common to encounter fuzzy data that contains numerous imprecise observations. The uncertainty associated with this type of data often leads to the use of interval statistical measures and the proposal of neutrosophic versions of probability distributions to better handle such data. We present a unique methodology that is based on the maximum likelihood approach and neutrosophic approach for estimating parameter of the proposed neutrosophic geometric distribution (NGD). The proposed methodology is supported by key likelihood inference results. The proposed distribution is specifically designed to handle variables with imprecise observation, hence effectively addressing a wide range of situations often encountered in the analysis of uncertain data. To evaluate the efficacy of the proposed neutrosophic model, we have carried out a comprehensive simulation experiment that rigorously examined the performance of the proposed model. The practical utility of NGD in the analysis of incomplete data is further exemplified through real-world applications.