Project managers often face different and conflicting objectives when optimizing project resources. In recent years, the demands of project stakeholders regarding reductions in the total cost and time of a project, along with achieving the acceptable quality of the project, have risen significantly. This factor leads researchers to develop models incorporating the quality factor into previously existing time-cost trade-off models. This paper develops a model for the discrete time-cost-quality trade-off problem. For each activity, an execution mode can be selected from a number of possible ones. The time and cost of each mode are assumed to be crisp, but the quality of each mode is a linguistic variable. Therefore, fuzzy logic theory is employed to consider the effects of uncertainty on project quality. Project managers can have different solutions depending on their accepted risk measure by applying α-cut methods in fuzzy logic theory. A new metaheuristic algorithm called NHGA has been developed to solve the model. A case example demonstrates the efficiency of the proposed algorithm for solving the model and its flexibility for project managers' decision-making. The proposed and classic genetic algorithms are prepared using the analysis of variance (ANOVA) method.