In order to solve the problem that the most linear power flow calculation methods can not deal with PV nodes, a linear power flow calculation method for distribution networks is proposed. Focused on the nodal power equations of polar coordinates’ Newton-Raphson power flow calculation, the proposed method uses linear approximation to handle the nonlinear terms in the nodal power equations according to the characteristics of distribution networks, and brings up a kind of linear power flow equation. The proposed method not only applies to weakly meshed networks, but also overcomes the defects that the most linear power flow calculation methods can not deal with PV nodes. The results of Newton-Raphson power flow calculation method is taken as a criterion, and the analysis of examples show that the magnitude of the maximum error of the proposed method is maintained at 10^-4. Computational accuracy and computational efficiency all meet the engineering demand of rapid analysis of distribution system. This work is supported by National Natural Science Foundation of China (No. 51467012).