In this paper, we studied the problem of link prediction in directed signed social networks.The relationships of these networks can be either positive (friendly) or negative (hostile) and the relationships are directed.We extended and generalized the commute time similarity of standard random walk theory in undirected unsigned networks to directed signed networks.We introduced and defined a Laplacian matrix in directed signed networks and proved that its Moore-Penrose pseudoinverse was a legal kernel to compute the nodes similarity.Motivated by the method of collaborative filtering, we proposed a link prediction method in directed signed networks to predict the links sign and direction based on the defined nodes similarity.We carried out experiments on two datasets from Epinions and Slashdot.Experimental results indicated that we got significant perfomance in temps of sign accuracy and AUC in the two real datasets.