This paper proposes a topology optimization method for modifying the zigzag micromixer to enhancing mixing. The reverse flow in the microchannels can enhance chaotic advection and make the passive micromixer mix better. Therefore the maximum of reverse flow rate turns into the objective function of the optimization problem. The zigzag micromixer is a hot model appearing in many papers. So modifying the zigzag structure for better performance is meaningful. By applying topology optimization method to the zigzag structure, a new micromixer, called TPZ, is created. Through lots of fruitful numerical simulations, TPZ is proved to be an outstanding micromixer with high homogeneity of the sample at various Reynolds numbers (Re). Although the pressure drop in TPZ is bigger than the zigzag micromixer at each Re inevitably, except special requirements, TPZ has potential application value in chemicals and biochemistry due to its outstanding mixing performance. For a wide range of Re (Re <= 0.5 or Re >= 5), TPZ delivers a great performance and the mixing index are all beyond 93%. Even in the range of 0.5-5 for the Re, the mixing index of TPZ is about 90%. (C) 2016 Elsevier B.V. All rights reserved.