Acoustic black holes (ABHs) have shown great potential in vibration and noise control. Merging the ABH effect and the metamaterial can be a more efficient approach for vibration control. The aim of this article is to study the dynamics of a metamaterial plate with crossed acoustic black holes. The band gap properties of the infinite structure and the influence of the design variables are investigated by using the finite element method and the Floquet–Bloch theorem. The vibration transmission and frequency response functions of the finite structure are presented to reveal the vibration attenuation mechanism. The effect of elastic boundary conditions on the vibration properties of the metamaterial plate is also studied. Numerical results demonstrate that the vibration is remarkably weakened due to the band gap and local modes induced by the ABH effect. Then, experimental validation is given by using 3D printing techniques. Finally, we study the multi-objective optimal design problem of the ABH plate to reduce the vibration amplitude and the structural mass simultaneously. Optimization results provide more options for the trade-off design of metamaterial plates between the lightweight design and vibration suppression capability.