A dual-band circularly polarised (CP) patch antenna with single layer and single feed is proposed. Different from other methods resorting to two dissimilar radiators, this antenna employs two pairs of degenerate modes, i.e. TM01/TM10 and TM03/TM30 modes, of a single radiator, making it compact size and geometrical symmetry. The antenna is composed of a square patch and four pairs of folded stubs at its four corners. The senses of CP radiation in the lower and upper bands are independently controlled, which can be the same or orthogonal. The influence of stubs loaded on the radiating patch and the design principle are given. To validate the design method, a prototype operating at 2.73 and 4.49 GHz is designed and fabricated. Measured results show that the right-hand CP and left-hand CP radiations can be obtained in the lower and upper bands. Measured results agree well with simulated ones, achieving the radiation gains of about 7.0 and 5.9 dBic in the two bands, respectively.