The main purpose of this paper is to determine the project completion time using a recursive method, where the activity times are distributed according to a sequence of beta distributions with unequal location parameters. For this purpose, we first evaluate the kth moment of the maximum of independent random variables that follow this sequence of distributions. Some illustrative examples are presented to demonstrate the applicability and appropriateness of this generalized beta model. These examples show that, the suggested estimate of project completion time is situated between the lower bound estimate (PERT) and the upper estimate that was obtained by Kambarowski. Moreover, this estimate has lowest variance among the other known estimates. Comparisons with other exemplary estimates (e.g., exponential, Erlang and Weibull estimates), discussed in literature, are presented.