A capacitor in a semiconductor device and a method for fabricating the same is disclosed. Disclosed the method for fabricating the capacitor in a semiconductor device comprises the steps of: forming a lower electrode made of doped silicon materials on a semiconductor substrate; depositing a thin silicon nitride layer on the lower electrode; forming a silicon oxynitride layer on the surface of the silicon nitride layer through oxidation of the silicon nitride layer; depositing a dielectric layer on the silicon oxynitride layer; and forming an upper electrode on the dielectric layer. According to the method, after the deposition of the silicon nitride layer on the dielectric layer, oxidation treatment of the resultant structure is performed and the dielectric layer is formed on the oxidized silicon nitride layer, thereby improving the interface characteristics between the lower electrode and the dielectric layer and resulting in a decrease of the leakage current and an increase of the breakdown voltage of the capacitor in the semiconductor device.