A novel planar circularly-polarized antenna using the stepped-width cross-dipole is presented in this paper. Firstly, the input impedance of a single stepped-width dipole is studied under different length and width ratios of two distinctive dipole sections. Then, two stepped-width dipoles with dissimilar dimensions are individually designed and orthogonally oriented in a crossed format, thus producing the circularly-polarized radiation. The entire antenna with a couple of dipoles is designed with a single feeding point. Our research work shows that the 10-dB bandwidth is about 25% in impedance and the axial ratio is less than 1 dB at the center frequency.