This paper addresses the flexible job shop scheduling problem with sequence-dependent setup times (SDSTFJSP). This is an extension of the classical job shop scheduling problem with many applications in real production environments. We propose an effective neighborhood structure for the problem, including feasibility and non improving conditions, as well as procedures for fast neighbor estimation. This neighborhood is embedded into a genetic algorithm hybridized with tabu search. We conducted an experimental study to compare the proposed algorithm with the state-of-the-art in the SDST-FJSP and also in the standard FJSP. In this study, our algorithm has obtained better results than those from other methods. Moreover, it has established new upper bounds for a number of instances.