Eigenvector　method　(EM)　is　a　well-known　approach　to　deriving　priorities　from　pairwise　comparison　matrices　in　the　analytic　hierarchy　process　(AHP),　which　requires　the　solution　of　a　set　of　nonlinear　eigenvalue　equations.　This　paper　proposes　an　approximate　solution　approach　to　the　EM　to　facilitate　its　computation.　We　refer　to　the　approach　as　a　linear　programming　approximation　to　the　EM,　or　LPAEM　for　short.　As　the　name　implies,　the　LPAEM　simplifies　the　nonlinear　eigenvalue　equations　as　a　linear　programming　for　solution.　It　produces　true　weights　for　perfectly　consistent　pairwise　comparison　matrices.　Numerical　examples　are　examined　to　show　the　validity　and　effectiveness　of　the　proposed　LPAEM　and　its　significant　advantages　over　a　recently　developed　linear　programming　method　entitled　LP-GW-AHP　in　rank　preservation.　(C)　2011　Elsevier　Inc.　All　rights　reserved.