The evolving High Voltage Direct Current (HVDC) technology integrated into the modern power grids can help improve operation stability and damp undesired low-frequency oscillations in the system. This paper presents a Power Oscillation Damping (POD) strategy for power systems with a hybrid (LCC-VSC) HVDC link. The work consists of a centralized supervision algorithm that monitors the dynamics of several system variables and sets the appropriate gains to the POD controller from a lookup table (LUT) generated offline via simulation-based Particle Swarm optimization analysis. The mathematical modeling for the test system with an embedded HVDC link is presented, and the optimal tuning problem is defined using performance-oriented objective functions. Details for the detection and scheduling algorithm, LUT construction, and controller structure are provided. The nonlinear simulation model is implemented in MATLAB, and the results support the effectiveness of the proposed approach.