Magnetic resonance electrical impedance tomography(MREIT) has been suggested to produce cross-sectional conductivity images of an electrically conducting object such as the human body. In most previous studies, recessed electrodes have been used to inject imaging currents into the object. An MRI scanner was used to capture induced magnetic flux density data inside the object and a conductivity image reconstruction algorithm was applied to the data. This paper reports the performance of a thin and flexible carbon-hydrogel electrode that replaces the bulky and rigid recessed electrode in previous studies. The new carbon-hydrogel electrode produces a negligible amount of artifacts in MR and conductivity images and significantly simplifies the experimental procedure. We can fabricate the electrode in different shapes and sizes. Adding a layer of conductive adhesive, we can easily attach the electrode on an irregular surface with an excellent contact. Using a pair of carbon-hydrogel electrodes with a large contact area, we may inject an imaging current with increased amplitude primarily due to a reduced average current density underneath the electrodes. Before we apply the new electrode to a human subject, we evaluated its performance by conducting MREIT imaging experiments of five swine legs. Reconstructed conductivity images of the swine legs show a good contrast among different muscles and bones. We suggest a future study of human experiments using the carbon-hydrogel electrode following the guideline proposed in this paper.