A two-dimensional (2D) periodic leaky-wave antenna (LWA) is proposed in this article. Using dielectric-filled wedge-like waveguide as medium for wave propagation, the quasi-TEM wave inside the guide is leaked through periodic rings of narrow slots, resulting in high gain frequency-dependent beam. Due to the two-dimensional nature of the antenna, along with the slots distribution, the radiation has low side lobe level (SLL) without the need to extend the length of the antenna as in the case of periodic one-dimensional (1D) LWA. The measured gain of the antenna is 20.34 dBi with SLL less than −13 dB and cross-polarization less the −28 dB. The antenna is proposed for millimeter-wave (mm-Wave) applications.