In a staggered erected cable-stayed bridge made of concrete, time-dependent phenomena (suchas creep or shrinkage) effects might play an important role in both its geometry and its stress state. In fact, because of these phenomena, stays will indeed lose force and higher bending moments will appear in the structure. To compensate these effects, one or two re-stressing operations are traditionally planned during the life time of long span cable- stayed bridges made of concrete. These re-stressing operations might be technologically challenging and always imply additional costs. To guarantee that allowable stresses and deflections are not exceeded during erection, a number of simulation methods are presented in the literature. Some of these methods, concretely those based on a backward simulation approach, fail addressing the effects of the timedependent phenomena. To simulate these effects, methods based on the forward simulation approach are traditionally followed. Nevertheless, the main trade-off of these algorithms is that their computation is based on complex iterative processes that make simulation more time consuming. Furthermore, these methods are not able to avoid the need of additional re-stressing operations in service to prevent the effects of the timedependent phenomena. To fill all these gaps, a new simulation algorithm, the Forward-Direct Algorithm (FDA), is formally presented in this paper to simulate the construction process of cable-stayed bridges including the time-dependent phenomena effects. This algorithm takes advantage of the unstressed length of the stays concept to carry out a computationally efficient simulation based on an innovative direct simulation approach. The major advantage of this algorithm is the fact that the prestressing operations during construction can be defined to avoid the need of additional re-tensioning operations in service. To illustrate the creep and shrinkage effects, the proposed algorithm is applied to a real cable-stayed bridge. This tool also can be used by the designer or the contractor for construction control of the strand by strand tensioning technique.