A model of the coupling of a Lambertian LED and a spherical‐ended fiber is proposed and analyzed by means of geometrical optics. The system of this optical coupling can be regarded as a simple optical system which consists of a light source, a principal plane, and an aperture stop. The model analyzed is that in which a light source and an aperture stop are on the anterior and the posterior focal planes, respectively. The maximum incident angle ϕm into the fiber is determined from the condition that the ray passing through the anterior focal point is not obstructed by the aperture stop, which has the same diameter as the core one. According to the theoretical analysis, the coupling efficiency for the Lambertian LED and the spherical‐ended fiber is sin2ϕm provided that d0?dc and (dc/d0)2 sin2ϕm provided that d0≳dc, where d0 is the emitting diameter and dc is the critical diameter defined by the critical angle ϕc of the light propagation in the fiber. For two kinds of LED’s with emitting diameters of 35 and 85 μm, the coupling experiment was performed on spherical‐ended fibers which had a numerical aperture NA of 0.14 and a core diameter of 85 μm. The spherical ends of fibers were fabricated to radii r from 75 to 170 μm. A good agreement between the theoretical and experimental results is obtained. In the case that the emitting diameter is 35 μm and the spherical radius is 75 μm, the calculated efficiciency is 6.3%, three times greater than that for a flat‐ended fiber. It is shown that the coupling efficiency can be improved by using the spherical‐ended fiber with the spherical radius less than about d1/(4NA), where d1 is the core diameter. It is also shown tha- t the maximum coupling efficiency for the LED with the emitting diameter of d0 is obtained by the fiber with the spherical radius less than about d0/(4NA).