It is well known over the recent years that measuring the success of projects under the umbrella of project management is inextricably linked with the associated cost, time, and quality. Most of the previous researches in the field assigned a separate mathematical model for each criterion, then numerical methods or search techniques were applied to obtain the optimal trade-off between the three criteria. However in this paper, the problem was addressed by linear multi-objective optimization using only one fuzzy mathematical model. The three criteria were merged in a single non-linear membership function to find the optimal trade-off. Finally, the proposed model is tested and validated using numerical examples.