A mode analysis is presented for the double-grating rectangular waveguide slow-wave structure (SWS) with arbitrary longitudinal displacements between the two gratings. By matching boundary conditions along the sides of the gratings, the distribution of electromagnetic field and high frequency characteristics of the SWS are studied. The simulation results show that the dispersion curve deduced from field equations is in good agreement with that simulated by software while the interaction impedance is higher than that calculated by HFSS, but lower than by CST. It also demonstrates that the longitudinal displacement between two gratings has a great effect on the first stop-band. The upper cutoff frequency of the first mode almost overlaps the lower cutoff frequency of the second mode when the displacement is set to be strictly half period, that is to say, the first stop-band disappears. To avoid the mode degeneracy and competition, the displacement is reduced to be about 0.45 times of period, so that with the interaction impedance kept unchanged, the stop-band increases about 7.9GHz, while the pass-band declines about 2.8 GHz.