We report on observation of simultaneous strong enhancements of second-harmonic generation (SHG) and third-harmonic generation (THG) in visible spectra region in a one-dimensional ZnSe-ZnMgS semiconductor photonic crystal. These enhancements come from phase matching and a high density of modes near the photonic band edge. Our result shows that the THG is due to direct χ(3) process instead of the cascaded two-step χ(2) process. Measured forward SH conversion efficiency close to 1% for only a few microns thick film demonstrates potential device applications. Theoretical calculations are in good agreement with the experimental measurements.