A hearing device includes a) a multitude of input transducers providing a corresponding multitude of electric input signals; and b) a processor for providing a processed signal in dependence of the electric input signals. The processor includes b1) a beamformer for providing a spatially filtered signal in dependence of electric input signals and beamformer filter coefficients determined in dependence of a fixed steering vector including as elements respective acoustic transfer functions from a target signal source, to each of said multitude of input transducers; and b2) a target adaptation module connected to the input transducers and to at least one beamformer, the target adaptation module being configured to provide compensation signals to compensate the electric input signals so that they match the fixed steering vector.