The design of a novel elliptically cylindrical transparent concentrator with functions of both electromagnetic transparency and electromagnetic concentration is put forward based on the form invariance of Maxwell’s equations in different coordinate transformation and transformation optics theory, and through the design of material constitutive parameters (permittivity and permeability) to guide the electromagnetic wave propagation. The electromagnetic wave transparent body does not prevent the transmission of electromagnetic waves that can interact in the cloak. An electromagnetic wave concentrator is an electromagnetic device that controls the electromagnetic waves to focus on an area or at a point to realize the electromagnetic wave energy concentration according to the requirement when the electromagnetic waves are incident on the device. In this paper, the expressions of the relative permittivity and permeability tensors in every layer of the electromagnetic device are derived by compression transformation and extension transformation. Then full-wave simulations for the electromagnetic device are performed by using finite-element software. The distributions of z-component of the magnetic field for the electromagnetic waves incident from different directions are obtained. Simulation results confirm the validity of the design method and the constitutive parameter tensors. Finally, effect of electromagnetic loss on the performance of the device is also discussed. To a certain extent, the function of the device will be weakened when the electromagnetic loss increases gradually. The design method proposed in this paper provides a new approach that can be used to design other novel electromagnetic devices.