A　matrix　is　called　a　complex-L　matrix　if　its　complex　sign　pattern　implies　that　it　is　of　full　column　rank.　The　definition　is　a　generalization　of　L-matrices　from　the　real　field　to　the　complex　field.　The　recognition　problem　of　complex-L　matrices　is　studied　in　this　paper;　a　combinatorial　characterization　of　complex-L　matrices　is　given,　showing　that　the　problem　of　recognizing　complex-L　matrices　is　in　the　class　co-NP-complete.　It　is　also　shown　that　this　recognition　problem　can　be　reduced　to　its　subproblem　for　which　each　entry　of　the　matrices　is　either　real　or　pure　imaginary.　(C)　2014　Elsevier　B.V.　All　rights　reserved.