The coupling of a spherical‐surfaced LED and a spherical‐ended fiber is analyzed using a model in which a light source and an aperture stop are on the anterior and posterior focal planes, respectively. The launching efficiency is defined as the ratio of the power launched into a fiber to the optical power generated in the LED. The efficiencies for step‐ and graded‐index fibers are derived. Maximum efficiency can be obtained whend0=dc, whered0is the emitting diameter anddcis the critical diameter defined by the focal length and the critical angle of the fiber. Whend0?dc, the ratio &khgr; of improvement in the efficiency for a spherical‐surfaced LED to that for a flat LED is approximately proportional to the square of the lateral magnification &bgr;, which is the image diameter divided byd0. &khgr;?&bgr;2is confirmed experimentally with couplings using spherical‐surfaced and flat LED’s.