We studied the growth process of Ge on a Si(113) surface by low energy electron microscopy (LEEM) combined with low energy electron diffraction (LEED). It is demonstrated that the transition from layer growth to island growth can be detected by the variation of the (00) spot intensity. The (00) spot intensity showed a minimum at around a coverage of 4.4 monolayer at about 560 C. Three-dimensional (3D) clusters form preferentially at the step bunches at the same coverage followed by the formation of 3D islands. This means that the. reduction of the (00) spot intensity is caused by the formation of 3D clusters while the growth of 3D islands whose center part shows bright contrast corresponds to the recovery of (00) intensity. The LEED patterns of the 3D islands show many spots originating from facets. The energy dependence of the spot positions reveals that the 3D islands have {15x} side facets.