A novel dual-band circularly-polarised microstrip antenna is proposed. The designs are based on the complementary two turns spiral resonator (CSR2). They are the counterparts of two turns spiral resonators (SR2s), which were introduced in 2004 by some of the present authors. The CSR2 technique can be applied to the design of miniaturised antenna by increasing electrical length. To demonstrate the idea, the proposed circularly-polarised antenna is designed to work at 658 MHz and 2.74 GHz. The gap orientation asymmetric or symmetric to the current propagating direction will render the antenna to radiate circular polarisation (CP) waves with the CSR2 etched on the antenna. Details of the experimental results compared with simulated results are presented and discussed.