Recently,　some　proximal-based　alternating　direction　methods　and　alternating　projection-based　prediction-correction　methods　were　proposed　to　solve　the　structured　variational　inequalities　in　Euclidean　space　.　We　note　that　the　proximal-based　alternating　direction　methods　need　to　solve　its　subproblems　exactly.　However,　the　subproblems　of　the　proximal-based　alternating　direction　methods　are　too　difficult　to　be　solved　exactly　in　many　practical　applications.　We　also　note　that　the　existing　alternating　projection　based　prediction-correction　methods　just　can　cope　with　the　case　that　the　underlying　mappings　are　Lipschitz　continuous.　However,　it　could　be　difficult　to　verify　their　Lipschitz　continuity　condition,　provided　that　the　available　information　is　only　the　mapping　values.　In　this　paper,　we　present　a　new　alternating　projection-based　prediction-correction　method　for　solving　the　structured　variational　inequalities,　where　the　underlying　mappings　are　continuous.　In　each　iteration,　we　first　employ　a　new　Armijo　linesearch　to　derive　the　predictors,　and　then　update　the　next　iterate　via　some　minor　computations.　Under　some　mild　assumptions,　we　establish　the　global　convergence　theorem　of　the　proposed　method.　Preliminary　numerical　results　are　also　reported　to　illustrate　the　effectiveness　of　the　proposed　method.