A highly regioselective synthesis of bicyclic sulfamides is described. Based on our recent discovery that bromoallenes can act as allyl dication equivalents in the presence of a palladium catalyst and alcohol, we investigated tandem cyclization of bromoallenes bearing a sulfamide group. It is found that some bromoallenes act as allyl dication equivalents even in the absence of a palladium(0) catalyst to afford cyclosulfamides containing five- or six-membered rings. While the palladium-free cyclization is dependent on the substrate structure affording the bicyclic sulfamides through the first cyclization onto the proximal or central carbon atom of the bromoallenes, the palladium-catalyzed reaction strongly promotes the first cyclization onto the central allenic carbon atom to afford bicyclic sulfamides containing a seven- or eight-membered ring. Formation of two types of bicyclic sulfamides from single bromoallenes by simply changing the reaction conditions is also described.