Time and cost are the main important attributes in construction projects in which they have trading off relations with together. Therefore, decision makers are dealing with the problem to organize the project completion time based on its overall cost. In the present research work, a non-linear programming model has been developed for considering the relationship between time and cost over the construction projects while the overall cost should be probably restricted on the specified base line. Trapezoidal fuzzy numbers have been used to define the relationship between time and cost in each activity, so a quadratic programming has been developed for considering time and cost trading off as well as probabilistic constraint on project overall cost. The proposed model has been applied in the case study of a construction project named Weigh in Motion system (WIM) and results revealed that probabilistic constraints and non-linear relations between time and cost can be formulated using a quadratic programming approach.