Abstract: Isogeometric topology optimization based on NURBS is one of the effective ways to implement the seamless integration between CAD and CAE as well as structural topology optimization, which can open up a new path for the development of our country industrial software. However, due to the high-order continuity and tensor product structure of NURBS basis functions, current isogeometric topology optimization methods cannot be directly applied to structural optimization problems of planar design domains with complex boundary. For solving the problem mentioned above, this work proposes a C¹ type multi-patch isogeometric topology optimization method for complex boundary planar design domains. The initial single-patch isogeometric mesh of the complex planar domain is generated by the combination of boundary correspondence algorithm and quasi-conformal parameterization method. To bypass the self-intersection problem existing in the generated single-patch isogeometric mesh, a DBSCAN-based partitioning method is proposed to generate multi-patch mesh with improved mesh quality. Moreover, the Lagrange multiplier method is applied to impose the geometric continuity constraints between different patches, which can address the issue of low geometric continuity between patches and ensure that the geometric continuity between different patches reaches C¹ continuity. According to the numerical examples of the dolphin bionic structure, wrench, and engine connecting rod, it indicates that the proposed method not only solves the problem of mesh self-intersection but also reduces the maximum value of the Beltrami coefficient modulus by more than 14%. Therefore, it significantly improves the quality of isogeometric meshes and, to a certain extent, enhances the convergence rate of topology optimization, which validate the effectiveness of the method proposed.