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The relationship between the branch powers and the node-injection powers were developed with the node-branch incidence matrix. Then based on two accurate formulas to estimate the voltage drop and angle difference, a new load flow algorithm for weakly meshed distribution systems was presented. By using active and reactive power rather than complex currents as flow variables, the algorithm reduces the computational complexity and has higher efficiency. Moreover, in order to deal with the PV nodes, a new solution was introduced based on Thevenin’s equivalent circuit. The solution deduced an accurate calculation formula to update the reactive power injections of PV nodes at each iteration and to fix voltage magnitude of PV nodes at specified values. The proposed load flow algorithm is essentially still belongs to the loop-analysis based method and has a strong ability to deal with meshed network. It reduces the iteration number and has a faster calculation speed even when network becomes more meshed and has more PV nodes. The numerical tests proved that the new method is robust and has excellent convergence characteristics.