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A new design for a dual-wideband circularly-polarised (CP) slot antenna with a modified tuning stub is presented. By adding an L-shaped strip and slit to the conventional L-shaped stub in the antenna with bandwidth (BW) of 49%, both impedance and CP BWs are considerably increased by up to 69%. Dual-wideband CP characteristic is then achieved by inserting another L-shaped slot into the tuning stub. Experimental results show that 3%dB CP and VSWR %2 impedance BWs are 18.9 and 21% for the lower band (3.5 GHz-WiMax) and also 32.5 and 33% for the higher band (5-6 GHz-WLAN/WiMax), respectively.