This paper aims to introduce a new concept which is Fermatean Neutrosophic Soft Set (FNSS), which is a combination of the Neutrosophic soft sets and Fermatean Fuzzy Sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of FNSS is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the most attractive laptop based on a computer simulation report. Finally, a comparative analysis between the initiated FNSS model and some existing approaches is provided to show its reliability.