This paper presents a novel approach to implement the robust minimum variance distortionless response (MVDR) beamformer. The robust MVDR beamformer is based on the optimization of worst-case performance and provides an excellent robustness against an arbitrary but norm-bounded desired signal steering vector mismatch. For real-time consideration, the beamformer was formulated into state-space observer form and the second-order extended (SOE) Kalman filter was derived. However, the SOE Kalman filter assumes an accurate system dynamic and statistics of the noise signals. These assumptions limit the performance under uncertainties. This paper develops the SOE H∞ filter for the implementation of the robust MVDR beamformer. The estimation criterion in the SOE H∞ filter design is to minimize the worst possible effects of the disturbance signals on the signal estimation errors without a prior knowledge of the disturbance signals statistics. Experimental results demonstrate the performance of the proposed algorithm in a noisy and reverberant environment and show its superiority of the robustness against mismatches over the robust MVDR beamformer based on the SOE Kalman filter.