Maximum radiation efficiency has been derived for homogeneous electrically small antennas. The spherical wave expansion is utilized to express the radiated field and the current distribution on an antenna, and the radiation efficiency is represented by the current, which is expressed in the spherical wave expansion coefficients and the nonradiating current. By using a concept of the nonradiating current, it is shown that the maximum radiation efficiency is achieved if the antenna shape is spherical. The radiation efficiency of a spherical antenna is maximized by varying the expansion coefficients. This radiation efficiency is compared with that of the antenna which achieves the maximum gain and those of linear antennas. The comparison indicates the validity of our proposed upper limit of the radiation efficiency.