In order to properly cover different scenarios, radiation patterns of antennas should be accordingly adjusted before fabrication. However, most antennas are unable to provide both broadside beam and designable conical beam which are usually-used radiation patterns for radio coverage. In this paper, a planar Circular Polarized (CP) annular Leaky-Wave Antenna (LWA) with conical beam is proposed, which is realized on annular Substrate-Integrated Waveguide (SIW). Broadside beam or conical beam could be easily obtained by fabricating the LWA with modified structural parameters. The central operating band is 5.8 GHz. The LWA allows only the -1th spatial harmonic to radiate, while the fundamental wave and other spatial harmonics are suppressed in slow wave mode. In order to validate the design effectiveness, two examples for broadside beam and conical beam radiation are fabricated and measured. The measurement results show good agreement with the simulation results. The proposed LWA presents a promising radiation performance and is a good candidate for wireless communication applications.