A new type of circularly polarized printed periodic leaky-wave antenna (LWA) structure with a wide scanning range and reduced sidelobe level (SLL) is presented. Fifteen matched unit cells (UCs) are cascaded along the direction of propagation to provide seamless frequency scanning from 20 to 29 GHz with a scanning range of 95° from backward to forward quadrant. The open-stopband has been suppressed around the broadside region by matching the input impedance of the UC to the characteristic impedance of the transmission line. Two empirical transmission line models are presented to describe the behavior of the periodic LWA. Parametric study using full-wave simulation is used to improve the SLL and minimize the axial ratio of the circular polarization leading to a fully optimized periodic leaky LWA.