A method for the super-resolution imaging of two-dimensional (2D) high-contrast targets is presented. There are two main methods to reconstruct unknown targets with super resolution. One is to illuminate the targets with specific incident fields and transform the information about the evanescent waves into the propagation waves, and the other is to adopt non-linear inversion methods where the multiple scattering within the objects are considered. For the specific-incident-field method, it has been proved that the orbital-angular-momentum (OAM)-carrying electromagnetic (EM) waves can be employed to image unknown targets with super resolution. In fact, OAM-carrying EM waves can transform the information about the evanescent waves into the propagation waves. Thus the resolution of imaging results can break the Rayleigh limit, namely super resolution. At present, the application of OAM-based super-resolution algorithm is only valid for weak scatters based on Born approximation. For the non-linear inversion methods, the contrast source inversion (CSI) is widely used to reconstruct unknown targets, including large-contrast or complex ones. In the CSI method, the information about the evanescent waves is naturally involved since the EM coupling within the objects is taken into account. Thus super resolution can also be achieved by the CSI method. This paper demonstrates a novel algorithm for super resolution of large-contrast targets by combining the OAM-based super-resolution technique and the CSI method. And the better resolution is achieved than by the CSI method. Firstly, 2D OAM EM waves are generated using uniform circular array of line source, and the region of interest is illuminated by the OAM beams of different topological charges. So the information about the evanescent waves can be converted into the propagation waves. Secondly, Born approximation is used to obtain the starting value of the contrast. In the process of evaluating the contrast, the super-resolution information is fully utilized. Thirdly, the starting value of the contrast source is evaluated using the starting value of the contrast. Then the CSI method starts to be iterated. Since the information about the evanescent waves is always involved in the iterating process, super-resolution reconstruction can be obtained and is better than that obtained by the CSI method. Numerical experiments show the accuracy of the algorithm by testing different scenarios. The resolution and outline of the target are reconstructed accurately even when the measurement data are corrupted by noise. To sum up, to reconstruct unknown targets with super resolution, one should firstly transform the information about the evanescent waves into the propagation waves, and secondly make full use of the super-resolution information in the inversion methods. The conclusion of this paper may provide an insight into the super resolution in EM inverse scattering.