The detailed design steps of a cylindrical leaky-wave antenna are presented. The configuration is assumed to be singly-curved, meaning that the curvature is constant in the longitudinal axis of the antenna. First, A CRLH (Composite Right/Left Handed) unit cell is designed on the planar structure for transition frequency 1.4 GHz and Bloch impedance near 50 Ω at the frequency range 1-3.5 GHz. Then, the resulting leaky-wave antenna on the planar structure which is composed of 10 unit-cells is transformed back to the conformal cylindrical configuration showing good agreement in their S-parameters and radiation patterns. The designed antenna has a satisfactory return loss in its radiation frequency range 1.2-2 GHz where its broadside radiation occurs at 1.4 GHz.