This paper investigates the budget variant of the discrete time/cost trade-off problem (DTCTP). This multi-mode project scheduling problem requires assigning modes to the activities of a project so that the total completion time is minimized and the budget and the precedence constraints are satisfied. This problem is often encountered in practice as timely completion of the projects without exceeding the budget is crucial. The contribution of this paper to the literatures is to describe an effective Benders Decomposition-based exact algorithm to solve the DTCTP instances of realistic sizes. Although Benders Decomposition often exhibits a very slow convergence, we have included several algorithmic features to enhance the performance of the proposed tailored approach. Computational results attest to the efficacy of the proposed algorithm, which can solve large-scale instances to optimality.