Differential beamformers with concentric circular microphone arrays (CCMAs) are desirable for use in various applications since they can form frequency-invariant spatial responses, have better beam steering flexibility than linear arrays, and suffer less with beampattern irregularity and white noise amplification than circular microphone arrays (CMAs). The methods developed previously for differential beamforming with CCMAs are based on the series expansion. Such methods need to know the analytic form of the target beam-pattern, which may not be accessible in practice. Furthermore, expansion error may lead to erroneous solution, which can cause noise amplification instead of reduction. In this paper, we extend our recently developed beamforming method for CMAs to the design of differential beamformers with CCMAs, which takes advantage of the symmetric null constraints from the beampattern. Simulations are performed to justify the properties of the proposed approach.