A novel multi-functional electromagnetic (EM) device named rotary-concentrator is designed based on transformation optics theory. For its ability to manipulate the EM wave in a special manner, it can rotate the propagation direction of the EM field in the core region to a fixed angle, as well as concentrate the EM energy into the core region simultaneously. For the proposed three equivalent configurations of the rotary-concentrator, the corresponding constitutive parameter expressions are derived respectively, and the full-wave simulations using the finite element software are also carried out. The simulated results validate the derived constitutive parameter expressions. For the three different kinds of configurations, the first two kinds consist of three layers of media, and the last one is simplified to a two-layer configuration. For a given arbitrary rotating angle and an energy concentration ratio, the three configurations can perform propagation direction rotating and energy concentrating in equivalent effect. These results contribute to further understanding of the mechanism of rotator and concentrator, and provide a fuller theoretical basis for the design of multi-functional devices. The proposed rotary-concentrator has potential applications in the design of high efficient receiving antennas and special circuit package interconnecting devices.