The solid-phase epitaxy (SPE) processes of amorphized Si surfaces by Ar+-ion bombardment are investigated in situ using a scanning tunneling microscope. As-bombarded Si(001) surfaces consist of grains 0.63-1.6 nm in diameter. The grains gradually coalesce and forms clusters 2-3.6 nm in diameter at an annealing temperature of 245-degrees-C. Prolonged annealing at this temperature promotes crystallization of the amorphous layers; (2X1) and (1X2) reconstructed regions surrounded by amorphous regions are partially observed on the surface, which suggests the onset of SPE. Successive observation reveals that the smoothing of the surface occurs layer by layer. As the annealing temperature is raised to 445-degrees-C, the amorphous layer epitaxially crystallizes up to the topmost surface, and a (2X1) reconstructed surface with monatomic height steps is observed. The smoothing of the step edges is observed during annealing at 500-degrees-C. The behavior of the defects during the recovery of crystallinity is also described.