This paper addresses a robust optimal damping control for the grid-forming converters. The proposed control strategy calculates the optimal damping and inertia parameters in form of constant gains via an Hinf-based static output feedback control synthesis. The capability and effectiveness of the proposed control methodology are proved by theoretical analysis, simulation, and experimental results on a typical grid-connected converter. It is shown that the designed controller can guarantee the robust performance and improves system stability. The simplicity of control structure, and providing desirable inertia and damping characteristics in a software program can be considered as the main advantages of the proposed methodology.