We have found the u-r color versus g-i color gradient space can be used for highly successful morphology classification of galaxies in the Sloan Digital Sky Survey. In this space, galaxies form well- separated early- and late-type branches. The location of galaxies along the branches reflects the degree and locality of star formation activity, and monotonically corresponds to the sequence of morphological subclasses. When the concentration index is also used, the completeness and reliability of classification reaches about 91% for a training set of SDSS galaxies brighter than r(pet) approximate to 15.9. At the faintest magnitudes (r(pet) approximate to 17.5) of the SDSS spectroscopic sample, the accuracy still remains at about 88%. The new classification scheme will help us find accurate relations of galaxy morphology with spatial and temporal environments, and help us to understand the origin of morphology of galaxies.