In this paper, we provide a state-space design method of H^∞ delayed feedback controller for MIMO plants. The underlying technical machinery is an extension of a state-space characterization of Nevanlinna-Pick interpolation via the J-lossless conjugation for the scalar case. By utilizing the state-space representation, the proposed algorithm avoids recursive computation with complex-valued matrices, which is required in the classical Nevanlinna algorithm. Our procedure also reduces the computational load specific to the delayed feedback controller design compared to the plant augmentation approach. Finally, the controller synthesis result is demonstrated through numerical simulations and experiments.