Radial line slot array (RLSA) antennas have attractive features, such as high gain, high efficiency, and planar low profile, but their gain-bandwidths have been limited to less than 10%. This article presents a method to significantly increase the gain-bandwidth of RLSAs to over 30%. The key to the method is the application of a nonuniform radial TEM waveguide as opposed to the radially uniform TEM waveguide used in conventional RLSAs. Hence, the condition for maximum radiation is satisfied at a wide range of frequencies by different sections of the RLSA. To demonstrate the concept, several circularly polarized RLSA designs and one prototype are presented. The measured results of the prototype demonstrate an unprecedented 3 dB gain-bandwidth of 27.6%, a peak gain of 27.3 dBic, 3 dB axial ratio bandwidth greater than 31.1%, and a 10 dB return loss bandwidth greater than 34.8%. The overall measured bandwidth of the RLSA in which gain variation and axial ratio are within 3 dB and return loss is greater than 10 dB is from 9.7 to 12.8 GHz or 27.6%. Its extremely high measured gain-bandwidth product per unit area (GBP/A) of 88 indicates excellent overall performance in terms of bandwidth, gain, and area.