The open column slow-wave grating structure, which is a novel type slow-wave system for Smith-Purcell FEL and relativistic TWT, was presented. The dispersion equation of the structure was derived by means of an approximate field-theory analysis, in which the continuous profile of the groove was approximately replaced by a series of rectangular steps, and the field continuity at the interface of two neighboring steps and the matching conditions at the interface between the groove region and central region were employed. The dispersion characteristics of the fundamental wave were numerically calculated and the effects of the geometrical dimensions of the grating on dispersion characteristics of system were also analyzed. And the simulation values of the structure, which is performed by using two-dimensional particle-in-cell code MAGIC, match the theoretical values very well.