Analysis and design of a coaxial leaky wave antenna with partially reflecting outer surface are presented. The leaky wave properties are controlled by adjusting the surface impedance of the outer surface, the filling dielectric constant and the dimensions of the inner and outer radii. The required surface impedance of the outer surface is implemented by using periodic slits in a perfect conducting outer cylinder. Simple analytical form is used to obtain the dimensions of theses periodic slits. An example for designing a coaxial leaky wave antenna is discussed in detail and is also verified and tuned up by using full wave numerical simulation.