The present invention has as its object to provide an iridium complex represented by the general formula: [(I r H L1 L2)2(μ−X1)(μ−X2)(μ−X3)]X4  (1) (wherein L1 and L2 may be the same or different and each represent a monodendate neutral ligand, or each cooperate with the other to form a bidendate neutral ligand; X1, X2 and X3 may be the same or different, and each represent a halogen atom; and X4 is a counter-anion). Also, the present invention provides a novel catalyst which can achieve excellent performance as a catalyst for asymmetric synthesis, especially asymmetric hydrogenation, in terms of chemical selectivity, enantioselectivity and catalytic activity, and the like.