In this paper, λI-statistical convergence is defined to generalize statistical convergence on Neutrosophic normed spaces. As it is known, Neutrosophic theory, which brings a new breath to daily life and complex scientific studies which we encounter with many uncertainties, is a rapidly developing field with many new study subjects. Thus, researchers show great interest in this philosophical approach and try to transfer related topics to this field quickly. For this purpose, in this study, besides the definition of λI-statistical convergence, the important features of Hilbert sequence space and λI-statistical convergence in Neutrosophic spaces are examined with the help of these defined sequences. By giving the relationship between Hilbert λI-statistical convergence and Hilbert I-statistical convergence, it has been evaluated whether the definitions contain a coverage relationship as in fuzzy and intuitionistic fuzzy. As a result, it is thought that the selected convergence type is suitable for the Neutrosophic normed space structure and is a guide for new convergence types.