A planar dual-band array with orthogonal circular polarizations (CP) in the two frequency bands is proposed in this paper. The array is implemented on a single-layer substrate and easy to be extended to design of a larger array. A new antenna element for such an array is exploited by symmetrically loading stubs on the edges of a square patch. In this work, two pairs of orthogonal modes of the patch, namely, TM10/TM01 and TM30/TM03, are excited simultaneously and used to realize different senses of CP radiation in the two bands. An equivalent transmission-line model of this patch is then developed to describe its working principle and design procedure. To validate its effectiveness, a 2×2-element array prototype operating at 2.53 and 3.59 GHz is designed and fabricated. Both the left- and right-hand CP, i.e., LHCP and RHCP, are obtained simultaneously in the dual bands, and the measured results are found to be in good agreement with the simulated ones. The measured radiation gains in the lower and higher bands are 10.8 and 12.5 dBic.