The Critical Path Method (CPM) is an important tool in project management. However, the traditional form of CPM deals with complications associated with the ambiguity and uncertainty in estimating the duration of activities. This paper presents two new methods to solve the Neutrosophic Critical Path Method (Neu-CPM), utilizing Triangular Neutrosophic Numbers (TNNs) to define activity durations under indeterminacy. The methods are designed to conduct a forward pass and backward pass simultaneously to find the earliest and latest time for each event while at the same time to find the total float for each activity, enabling project scheduling under uncertain conditions. Neu-CPM provides a more improved approach to handling non-precise and incomplete data compared to the traditional fuzzy or intuitionistic approaches, based on its inclusion of membership degrees of truth, indeterminacy, and falsity. A numerical example is provided showing the methodology’s ability to identify the project’s critical path in a neutrosophic environment while studying the effect of various risk elements on the critical path. The results show that Neu-CPM provides the opportunity of more flexibility, accuracy, and reliability in project scheduling in uncertain conditions, with useful applications to practice.