The critical path method (CPM) is an important tool for the planning and control of the large projects and projects that are complex in nature. Clear determination of time duration will help to implement the CPM successfully. But in real life, the time duration cannot be determined crisply. Hence there is always an uncertainty about the time duration of activities which leads to the development of fuzzy critical path method. In this article, a wavelet based ranking namely, Haar ranking for fuzzy numbers is applied to order the fuzzy numbers. In this algorithm first the fuzzy parameters are converted in to Haar tuples using Haar wavelet technique and critical path method is applied to get the solution. The proposed method is easy to understand and implement, as it follows the standard steps of the regular critical path method. A Practical example is given and the solution strongly suggests that the proposed method gives us the fuzzy critical path and also identifies the critical activities and red flag activities. © BEIESP.