This paper presents a numerical study conducted on a seven-story timber building made of cross-laminated (X-lam) panels, equipped with a linear translational tuned mass damper (TMD). The TMD is placed on the top of the building as a technique for reducing the notoriously high drifts and seismic accelerations of these types of structures. TMD parameters (mass, stiffness, and damping) were designed using a genetic algorithm (GA) technique by optimizing the structural response under seven recorded earthquake ground motions compatible, on average, with a predefined elastic spectrum. Time-history dynamic analyses were carried out on a simplified two-degree-offreedom system equivalent to the multistory building, while a detailed model of the entire building using two-dimensional elastic shell elements and elastic springs for modeling connections was used as a verification of the evaluated solution. Several comparisons between the response of the structure with and without TMD subjected to medium- and high-intensity recorded earthquake ground motions are presented, and the effectiveness and limits of these devices for improving the seismic performance of X-lam buildings are critically evaluated.