The modes of electromagnetic surface waves sustained by the edge of a photonic crystal slab consisting of a honeycomb array of gyromagnetic material columns were investigated when an external dc magnetic field was applied to it. It is firstly demonstrated that in the photonic band structure of this photonic crystal slab, the original degeneracy point of the lowest two (photonic) energy curves can be lifted by applying an external magnetic field, thus forming a band gap between the two bands. Furthermore, it is demonstrated that based on this sort of band gap, surface mode sustained by the edge of the photonic crystal slab can propagate only in one direction, attributing to the time-reversal symmetry of the system broken by the external magnetic field. With the effective total internal reflection effect, the unidirectional edge mode in this three-dimensional system is confined in the direction normal to the photonic crystal slab.