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 calculated from an estimated source position. The soft constraint secures the spatial-temporal passage of the desired source signal in the adaptive update of the beamforming weights and guaranties the full rank property of the covariance matrix inverted in the update. This approach allows for an efficient adaptation of the beamformer to speaker movement by using a tracking algorithm for sound source time-delay estimation. The proposed method has the benefit of taking into consideration the discrepancies in the acoustical environment model as well as errors in the time-delay estimation. Evaluation in a real environment with a moving speaker in a hands-free situation shows up to 10~dB noise suppression and 20~dB interference suppression within the conventional telephone bandwidth. This is achieved with a negligible impact on target signal distortion.