Critical Path Method (CPM) technique has become widely recognized as valuable tool for the planning and scheduling large construction projects. The aim of this paper is to present an analytical method for finding the Critical Path in the precedence network diagram where the duration of each activity is represented by a trapezoidal fuzzy number. This Fuzzy Critical Path Method (FCPM) uses a defuzzification formula for trapezoidal fuzzy number and applies it on the total float (slack time) for each activity in the fuzzy precedence network to find the critical path. The method presented in this paper is very effective in determining the critical activities and finding the critical paths.