Superdirectional acoustic beamforming technology provides a high signal-to-noise ratio, but potential speech intelligibility benefits to hearing aid users are limited by the way the users move their heads. Steering the beamformer using eye gaze instead of head orientation could mitigate this problem. This study investigated the intelligibility of target speech with a dynamically changing direction when heard through gaze-controlled (GAZE) or head-controlled (HEAD) superdirectional simulated beamformers. The beamformer provided frequency-independent noise attenuation of either 8 dB (WIDE [moderately directional]) or 12 dB (NARROW [highly directional]) relative to no beamformer referred as the OMNI (omni-directional) condition. Before the main experiment, signal-to-noise ratios were normalized for each participant and each beam width condition to yield equal percentage of correct performance in a reference condition. Hence, results are presented as normalized speech intelligibility (NSI). In an ongoing presentation, the participants ( n = 17), of varying degree of hearing loss, heard single-word targets every 1.5 s coming from either left (−30°) or right (+30°) presented in continuous, spatially distributed, speech-shaped noise. When the target was static, NSI was better in the GAZE than in the HEAD condition, but only when the beam was NARROW. When the target switched location without warning, NSI performance dropped. In this case, the WIDE HEAD condition provided the best average NSI performance, because some participants tended to orient their head in between the targets, allowing them to hear out the target regardless of location. The difference in NSI between GAZE and HEAD conditions for individual participants was related to the observed head-orientation strategy, which varied widely across participants.