Topology is a branch of mathematic that deals with the specific definitions given for spatial structure concepts, com-pares different definitions and explores the connections between the structures described on the sets. Also, neutrosophic triplet metric and neutrosophic triplet topology are a new concept in neutrosophy and they are completely different from classical structures. In this paper, we firstly study neutrosophic triplet metric topology. Furthermore, we give some new definitions and properties for neutrosophic triplet metric space, neutrosophic triplet topology and neutrosophic triplet metric topology. Thus, we obtain neutrosophic triplet metric topology using the neutrosophic triplet metric and neutrosophic triplet topology. Also, we show relationship between neutrosophic triplet metric space and neutrosophic triplet topology.