The present invention is related to a structure of a display device. More particularly, the present invention is related to a display device having an electrode structure. In the existing display device such as an organic light-emitting display (OLED), a thin film transistor (TFT) panel (TFT-PANEL) and a color filter panel (CFT-PANEL) are generally formed on two glass substrates respectively, wherein the TFT-PANEL is used as a display area for displaying pictures, and the CFT-PANEL is used as a color filter area for displaying colors. Thus, if it is intended to form a high resolution picture, both the panel resolution and the aperture rate (i.e., aperture ratio) of the display area become increased, which limits the aperture rate of the color filter area; this will cause the panel to have a limited color gamut, thereby leading to reduced color saturation of pictures. Besides, if the resolution of the display area is not increased along with the increased aperture rate of the color filter area, the color filter area will have to be enlarged, which inevitably limits the size of the display area. As shown in FIG. 1, U.S. Pat. No. 5,596,204 discloses a method for manufacturing an electrode structure of an OLED display device. In this patent, a TFT area 2 is formed on a glass substrate 1, and then an ITO transparent electrode 3 is formed. In the next process, a color filter area 4 is formed on the glass substrate 1, wherein color film units are disposed in the color filter area 4. After the steps of forming the color film units, a passivation area 5 is formed in the glass substrate 1 and an ITO electrode 6 is formed. The purpose of the passivation area 5 is to block moisture or the like from getting into the color film units, and the electrode 6 is used to be an anode electrode for injecting holes. The electrode 6 is not in connection with the ITO transparent electrode 3, and therefore the step of forming the electrode 6 does not influence the ITO transparent electrode 3. Therefore, the ITO transparent electrode 3 will not suffer from corrosion due to moisture or the like in the process of forming the electrode 6. However, in the manufacturing method as described in U.S. Pat. No. 5,596,204, since the ITO electrode is a transparent electrode, the electrode has to be in connection with the color film units, and the material of the electrode has to be a transparent material; otherwise, the pixel electrode will have to be made of an opaque electrode. In other words, the transparent electrode 3 and the color film units (the color filter 4) are simultaneously formed by coating or vapor deposition, and therefore the ITO electrode 3 is often to be electrically connected with the color film units (the color filter 4). In addition, the ITO transparent electrode 3 has to be kept in connection with the color film units (the color filter 4) via a conductive barrier layer (for example, an insulating layer made of SiNx), and this requirement will make the manufacturing process more complicated. In another example, in order to improve the aperture rate of the display area of a display device, U.S. Pat. No. 6,268,856 discloses a display device having a transparent electrode with two or more layers. However, in the process of forming the transparent electrode with two or more layers, an insulating film has to be made of an organic material; otherwise, it will be difficult to form the transparent electrode having the two or more layers. In addition, since the transparent electrode is an organic film, it will be oxidized when it is exposed to atmosphere for a long time, and therefore a corrosion resistant layer has to be made of an organic material in order to prevent from being oxidized. In the course of the manufacturing process, however, since the insulating film of the organic material is required to be thick enough to passivate the transparent electrode in a proper condition; therefore, there is usually little space for depositing the corrosion resistant layer and therefore the corrosion resistant layer will be easy to get into short circuit with the electrodes. Besides, due to the use of the organic material, the whole manufacturing process will be more complicated, and a lot of time will be required to develop the technology and the processes used in the manufacturing process. It is a drawback of the prior art that when the color filter area is used to display colors, the transparent electrode may suffer from corrosion due to moisture in the air, which may greatly influence the performance of the display device. Therefore, there is a need to improve the display device to avoid from the problem caused by corrosion.