The frequency invariant beamformer (FIB) finds important applications such as in distortionless acoustic signal acquisition, et al. Conventional FIB design approaches are usually proposed with ideal microphone array models, i.e., there are no gain and phase mismatches in microphone array characteristics. Therefore, the performance of the conventional FIBs will degrade in practical applications. In this paper, a robust FIB design approach based on regularized constrained least squares are presented, which can work well in the presence of microphone mismatches. The proposed approach is applicable to arbitrary array geometries, and it also has a closed-form solution, so there is no need for iterative computation, which leads to a lower computational complexity in design. Several design examples are presented to show the effectiveness of the proposed approach as well as the correctness of the theoretical analysis.