The frequency invariant beamformer (FIB) is of great interest in practice for distortionless broadband audio signal acquisition and processing. One of the representative approaches recently proposed for FIB design is the least squares method based on the spatial response variation (LS-SRV). It is noted that the performance of the LS-SRV is dependent on the tap length of FIR. By increasing the FIR tap length, the FIB performance can be effectively improved. However, this is at the cost of greater implementation complexity. To combat this problem, we proposed in this paper an improved design scheme with sparse FIR tap coefficients. Our proposed approach is based on the iterative reweighted minimization from signal sparse representation. The efficacy of the proposed method has been evaluated by design examples.