Damping behaviors of granular particles in a quasi-two-dimensional (Q-2D) closed container subjected to vertical vibration are simulated by means of Discrete Element Method (DEM). Phase diagram and damping contour of vibrated granular particles in the amplitude-frequency plane of external excitation are obtained, which indicates six different damping phases of vibrated granular particles. Simulation results also reveal that three suspended states of vibrated granular particles (i.e., Leidenfrost effect, Buoyancy convection and Bidirectional Leidenfrost effect) display the higher damping capacity, and especially granular Leidenfrost effect demonstrates the optimal damping effect. Furthermore, the dissipation characteristic of granular Leidenfrost effect is analyzed respectively from the perspective of energy transformation and energy dissipation. The influence of the corresponding parameters (gap clearance, particle diameter and container dimension) on the three high damping suspended phases (HDSPs) of vibrated granular particles is explored. Finally, base on the rheological behavior of vibrated granular particles, a visualization method for evaluating the granular damping effect by DEM simulation is proposed for the first time, which may provide a new idea for designing optimal granular dampers. (C) 2017 Elsevier B.V. All rights reserved.