As　one　kind　of　terahertz　sources,　the　cross-field　backward　wave　oscillator　requires　a　slow-wave　structure　(SWS)　to　transmit　electromagnetic　waves　which　is　difficult　to　fabricate.　This　paper　describes　the　performance　of　the　open　rectangular　grating　wave　guide　SWS　in　terahertz　and　the　design　of　SWSs.　By　using　field-matching　method,　the　dispersion　equation　and　the　average　coupling　impendence　expression　are　obtained　and　solved.　And　the　length　of　the　period　of　SWSs　is　considered　to　be　important　because　the　coupling　impedance　can　be　optimized　by　simply　changing　it　without　other　adverse　effects.　The　process　and　results　of　design　of　SWSs　are　summarized　and　verified　by　a　simulation　using　PIC　method　and　all　the　results　included　different　structures　with　distances　between　two　comb　teeth　ranging　from　0.01　to　0.025　mm,　and　the　frequencies　ranging　from　300　to　420　GHz.