Non-layered two-dimensional structures with the atomic thickness recently attract much attention. In this work, we predicated a two-dimensional structure of non-layered ScC, denoted as ScC sheet, and evaluated its potential as the electrode material of Na-ion battery. The stability of ScC sheet is determined by the cohesive energy, phonon spectrum and potential energy curve calculations. Interestingly, the proposed ScC sheet can exhibit many unexpected electrochemical properties. It is found that ScC sheet can possess strong Na adsorption capability. Both pristine and Na-interacted ScC sheets represent good electronic conductivity due to the metallic nature. The structural degradation of the ScC during the sodiation and desodiation processes will not be anticipated. Besides, our results reveal that the ScC sheet has a minimal diffusion barrier of 9 meV and the calculated theoretical capacity of ScC sheet can reach to 940 mAh.g(-1) on the basic of the second layer adsorption. Thus, benefiting from these features, ScC sheet is expectable to be served as a promising electrode material for the Na-ion battery.