Smith-Purcell radiation from a charge running near a photonic crystal is calculated for a slab system of a periodic array of dielectric spheres, with the photonic band effect taken into account exactly. The radiation spectrum has a series of resonantly enhanced structures, which are shown to arise accompanying the excitation of the photonic bands. It is also shown that the overall intensity of the emission band does not depend very strongly on the slab thickness but the height of the resonant peaks increases progressively with thickness due to the enhanced Q value of excited photonic bands.