To address the medium- and high-frequency oscillations in modular multilevel converter (MMC) based flexible DC transmission systems, a medium and high-frequency oscillation suppression strategy is proposed from the perspective of converter-station admittance passivity, aiming to eliminate such oscillations in flexible DC systems. First, an MMC admittance matrix model considering the frequency coupling effect is established, and the intrinsic relationship between the passivity of the MMC admittance matrix and the stability of the flexible DC system is clarified. Second, following the fundamental principle of the coordinated suppression strategy, active damping is introduced to shift the non-passive frequency region of the MMC towards higher frequencies. Subsequently, the influence of active damping integrated into different control loops on the passivity of the MMC admittance matrix is quantitatively analyzed, thereby determining the type of active damping and its optimal insertion point. The damping parameters are then selected using an exhaustive search method with the objective of maximizing the upward shift of the non-passive frequency region. Furthermore, under the prerequisite of ensuring the passivity of the flexible DC system, the parameters of the passive damping are designed using an optimization algorithm, with the reactive power compensation requirement and active power losses of the passive damping as the objective functions, thereby achieving a balance between system stability and economic performance. Finally, a simulation model of the flexible DC transmission system is established in MATLAB/Simulink to validate the correctness of the MMC admittance matrix model and the effectiveness of the proposed suppression strategy.