Electroosmotic flow is one of the commonly used driving mechanisms for microfluidics in current chip laboratory equipment， and the electrode layout plays an important role in controlling the external electric field driven by electroosmotic flow. At present， the layout of an electroosmotic flow electrode is mostly designed based on size optimization and shape optimization， making it difficult to improve the performance of microfluidic devices. To solve this problem， a topology optimization model of an electroosmotic flow electrode is established. The filter equation and threshold projection are used to control the characteristic size of the electrode structure. The adjoint sensitivity of the model is obtained by a continuous adjoint analysis method， and then the structural design variables of electrode layout are developed. Finally， the topology of an electroosmotic flow electrode is optimized. Based on this topology optimization method， the electrode layout of an electroosmotic flow micromixer was designed， and the factors affecting its mixing effect were analyzed. The results show that the mixing evaluation index of the electroosmotic flow micromixer reaches 0.047， which can completely mix two different concentration solutions. The good mixing performance of the micromixer verifies the effectiveness of the proposed electroosmotic flow method for electrode topology optimization.