This article presents a new configuration of the bull-eye leaky wave antennas by replacing metal rings with dielectric rings. The periodic surface is composed of double concentric dielectric rings used for generating a broadside pencil beam. A parametric study of the effect of the height of the rings is first presented analysing the dispersion characteristic for both the TE and the TM leaky-modes supported by the cylindrical rings. Afterwards, two antenna designs made with different values for the height of the rings are presented with results obtained by full-wave simulations. The selected final design exhibits a highgain symmetrical broadside pencil beam and it is prepared to be manufactured by simple cost effective 3D printing technology.