Abstract: The linear power flow calculation method can provide better robustness and higher efficiency for active distribution network analysis and operation regulation. In this paper, a new three-phase unbalanced linear power flow calculation method is proposed. The voltage magnitude of the three-phase power flow equation is transformed into logarithmic form under polar coordinates. And then a reasonable linear approximation is formed according to the actual characteristics of the three-phase distribution network. The proposed method avoids iterating and can directly calculate the three-phase unbalanced power flow of the radial and weak-loop distribution networks as well as the distribution networks containing PV nodes.The proposed method is tested and compared through an IEEE33 three-phase unbalanced example, and its effectiveness has been verified.