With the development of power electronics technology, a high proportion of new energy is connected to the distribution network, which makes the voltage distortion of the power system serious. In previous studies of harmonic state estimation (HSE), a grid is often estimated as a whole. However, for grids with uneven distribution of measurement devices and lack of measurement, the harmonic state estimation of the whole grid often leads to an increase in the error of the results. In this paper, a partitioning algorithm based on the weighted least squares estimation (PWLSE) is proposed to estimate the harmonic states of radial grids. The algorithm divides the distribution network into the core measurement region and local regions. Firstly, the harmonic state estimation is performed for the core measurement region with sufficient measurement data. Then, in the local region, estimate the data of the nodes that lack measurement. Finally, the harmonic state estimation is performed for the local regions respectively. The proposed algorithm is validated through simulation cases, which show that the proposed method is more suitable for the radial distribution network and greatly reduces the computational workload compared with the traditional harmonic state estimation method.