Parrondo's paradox occurs in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. Several variations of Parrondo's games with paradoxical property have been introduced. In this paper, I examine whether Parrondo's paradox occurs or not in scale free networks. Two models are discussed by some theoretical analyses and computer simulations. As a result, I prove that Parrondo's paradox occurs only in the second model.