In this paper we consider a certain kind of linear programming problems. This kind, in which fuzzy complex number is the coefficient of the objective function, is called fuzzy complex linear programming problem. Solutions of this kind of problems will be characterized by deriving its fuzzy Kuhn-Tucker conditions. The results include a duality relation between α -cut programming and its dual are discussed. Also, we introduce the proof of Kuhn-Tucker stationarypoint necessary optimality theorem for our problem.