Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralities as well as their interactions with different ideational spectra.  Neutrosophic sets have been introduced as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets to represent uncertain, inconsistent and incomplete information about real world problems. Elements of neutrosophic set are characterized by a truth-membership, falsity-membership and indeterminacy membership functions. Neutrosophic set theory is applied in multi attribute decision making problems. In this paper, project network in neutrosophic environment is proposed with the introduction of a new ranking method to solve critical path problem where the activity durations are in the form of do-decagonal neutrosophic number. The critical path problem is one of the several related techniques for planning and managing of complicated projects in real world applications. Comparing to the conventional ranking methods we got a better result using the new ranking method. Further an illustrative example is provided to validate the proposed approach.