Interleaved antenna arrays are widely used in radar tracking, navigation, wireless communications, and location, etc. In order to make use of a given antenna aperture of concentric rings array (CRA) efficiently, an interleaved method for interlacing uniform CRA is proposed in this paper based on Subarray element Excitation-Matching (SEM). Due to Fourier-Bessel transform mapping between array factor and uniform CRA antenna excitation, in our method, the array factor of CRA is first calculated and its sidelobe region is then amended accordingly to meet user-defined sidelobe level threshold. In the next steps, the updated antenna element excitation coefficients are acquired with 2-D fast Fourier transform (FFT) and cubic interpolation method. Finally, with a careful exploration of the excitation distributions, the antenna positions of thinned subarrays are deliberately chosen in an alternating manner, which ensures that a similar pattern can be achieved with different thinned subarrays. The performance of the proposed interleaved CRA design method is evaluated by numerical simulation.