The critical path method (CPM) is a project modelling algorithm developed in the 1950s for scheduling project activities, it is used to determine the critical path through the calculation of three parameters thus, slack, earliest event, latest event times for each activity. In this paper, we demonstrate how to use Tawanda's non-iterative optimal tree algorithm for shortest route problems (TA) to determine the critical path(s). We have also compared TA with the original critical path method (CPM) and the modified Dijksra's algorithm for critical path method in a project network (MDA). However, the study revealed that TA can compute the critical path more effectively since it is also effective in project networks with k-possible critical paths, moreover, it does not make use of the slack, earliest, and latest time parameters, since these calculations consume more time.