This paper presents a new constrained subband beamforming algorithm to enhance speech signals generated by a moving source in a noisy environment. The beamformer is based on the principle of a soft constraint defined for a specified region corresponding to a known source location. The soft constraint secures the spatial-temporal passage of the desired source signal in the adaptive update of the beamforming weights and guarantees the full rank property of the matrix inverted in the update. The source of interest is modelled as a cluster of stationary point sources and source motion is accommodated by revising the point source cluster. The source modelling and its direct exploitation in the beamformer through covariance estimates are presented. An algorithm for sound source localization is used for speaker movement tracking and this information is exploited to update the spatial distribution in the source model. Evaluation in a real environment with a moving speaker shows a significant noise and hands-free interference suppression within the conventional telephone bandwidth. This is achieved with a negligible impact on speech distortion.