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.　©　2014　Elsevier　B.V.　All　rights　reserved.