In this paper, a novel subband-selective generalized sidelobe canceller (GSC) for partially adaptive broadband beamforming is proposed. The columns of the blocking matrix are derived from a prototype vector by cosine-modulation, and the broadside constraint is incorporated by imposing zeros on the prototype vector appropriately. These columns constitute a series of bandpass filters, which select signals with specific angles of arrival and frequencies. This results in highpass-type bandlimited spectra of the blocking matrix outputs, which is further exploited by subbands decomposition and suitably discarding the low-pass subbands prior to running independent unconstrained adaptive filters in each non-redundant subband. By these steps, the computational complexity of a GSC implementation is greatly reduced compared to fully adaptive GSC schemes, while performance is comparable or even enhanced due to subband decorrelation in both spatial and temporal domains.