Electromagnetic scattering by finite number of conducting strips loaded on a grounded dielectric is considered for the TM polarization case from the viewpoints of transmitting(receiving) leaky wave antenna and grating coupler. An integro-differential equation whose unknowns are the induced currents over the strips is derived and solved by use of the method of moments. In order to construct the non-uniform leaky wave structures with specific source(current) distributions over the strips, distances between two adjacent strips and strip width are simultaneously varied along the structure. From some results for the current distributions over the strips and surface wave powers, it is observed that the maximum coupling efficiencies of the appropriately constructed non-uniform leaky wave structures from the viewpoints of both a receiving leaky wave antenna and a grating coupler amount upto 95%, which are about 15% improvements compared with those(80%) of the uniform structures.