A tuned mass damper (TMD) is one of the oldest and most commonly used passive control devices attached to structures to absorb lateral loads of energy from main systems. In the last decades, several novel tuned mass dampers have been designed to increase the performance of TMDs in decreasing the structural responses during excitation vibrations. Moreover, several formulations and numerical optimization methods have been developed to optimize the TMDs parameters. This paper proposes a novel passive tuned mass damper with dual stiffness (DSTMD). The DSTMD includes mass, primary and secondary springs, dashpot, and motion limiting chamber. The performance of DSTMDs depends on their properties such as mass, primary and secondary stiffness, damping coefficient, and the length of the motion limiting chamber. Thus, a metaheuristic optimization algorithm, called the Mouth Brooding Fish algorithm, was used to optimize the DSTMDs parameters. The effectiveness of the optimum DSTMD on two different linear ten-story structures under several earthquakes has been studied and compared with the effectiveness of classical optimum TMDs. According to the study, optimum DSTMDs generally show better effects for certain excitations, and as an average performance, they are superior compared to the classical optimum TMDs in reducing maximum displacement of the buildings. At last, structural yielding is considered, and the performance analysis on this structure shows that the DSTMD has a superior effect in reducing the maximum displacement and is among the best methods for the calculated absolute yielding amount.