This paper presents a computationally tractable moving horizon H-infinity control scheme, where the to be on-line solved minimax problem is relaxed to a minimization problem by Lagrange duality. This helps the avoidance of infeasibility and reduction of conservation caused by the ellipsoid evaluation of time-domain constraints. Disturbance attenuation with performance adaptation is achieved by on-line monitoring of the dissipation level and accumulating the 'energy reserve' from performance relaxations that are necessary for the satisfaction of time-domain constraints. Simulation and comparison results confirm the advantages of the proposed algorithm.