In　this　article,　a　new　method　is　proposed　for　solving　a　class　of　structured　variational　inequalities　(SVIs).　The　proposed　method　is　referred　to　as　the　partial　inexact　proximal　alternating　direction　(piPAD)　method.　In　the　method,　two　subproblems　are　solved　independently.　One　is　handled　by　an　inexact　proximal　point　method　and　the　other　is　solved　directly.　This　feature　is　the　major　difference　between　the　proposed　method　and　some　existing　alternating　direction-like　methods.　The　convergence　of　the　piPAD　method　is　proved.　Two　examples　of　the　modern　convex　optimization　problem　arising　from　engineering　and　information　sciences,　which　can　be　reformulated　into　the　encountered　SVIs,　are　presented　to　demonstrate　the　applicability　of　the　piPAD　method.　Also,　some　preliminary　numerical　results　are　reported　to　validate　the　feasibility　and　efficiency　of　the　piPAD　method.