A new type of array signal processing combined with a weighted least squares algorithm to enable two-channel output with binaural information is proposed in this paper. This algorithm may be effective for use in a binaural hearing aid because the interaural relationship can be preserved after array signal processing. Retaining spatial information on specified directions while sufficiently suppressing unnecessary ambient noise coming from directions other than those of target sounds is required for this type of algorithm. In order to satisfy these two simultaneous requirements, the proposed algorithm was derived from a constraint algorithm by employing the weighted least squares algorithm. Performance in directivity patterns as well as interaural time difference (ITD) and interaural level difference (ILD) were evaluated. Computer simulations showed that this algorithm yields robust performance in various conditions compared with array signal processing based on a constraint algorithm.