The perfectly matched layer plays a key role in electromagnetic simulations, and it makes the infinite space look like a finite space, so that the electromagnetic waves propagating to the boundary seem like their propagations to the infinity. The inner perfectly matched layer has a similar concept, usually in the form of a cylinder or sphere placed inside the physical field. It makes the electromagnetic field matched at the boundary, so that the electromagnetic waves propagate on its convex surface as if they were propagating to an infinite distance, without any scattering. In addition to the perfectly matched layer, planar absorbers can be realized in a variety of ways, such as spatial Kramers-Kronig relations, photonic crystals, metamaterials, etc. On the other hand, the inner cylindrical or spherical absorbers are generally perfect absorbers, electromagnetic “black hole”, etc. Transformation optics always arouse great research interests. For its property of controlling propagation of electromagnetic waves arbitrarily under coordinate mappings, transformation optics has a wide range of applications and has also been used as a theoretical tool for designing absorbers. However, to the authors’ knowledge, there is no effective method to achieve perfect absorption of inner absorbers with no reflections and independence of incident angle or wave frequency. In this paper, transformation optics theory is used to design an inner perfectly matched layer whose material parameters are obtained by a radial coordinate transformation of the complex plane. Through investigating the electromagnetic wave patterns and the two-dimensional far-field diagrams, we intuitively compare and analyse one by one the absorption characteristics of the matched and mismatched perfect absorber, electromagnetic “black hole” and the inner perfectly matched layer. It is found that the matched perfect absorber has better absorption property than mismatched one and electromagnetic “black hole”. In the electromagnetic “black hole” there appear a lot of scatterings. While our inner perfectly matched layer demonstrates the best effectiveness of absorption with no back scattering. It can be used as an absorbing kernel in electromagnetic simulations and relevant experiments.