Because of the traditional power distribution network fault location requires a large amount of measuring point information, but the power distribution network structure is complex and the number of measuring devices is small, this paper proposes a new method that only needs to install some measuring points in the power distribution network, then locating the fault based on graph regularization and Iteratively reweighted least squares (IRLS) algorithm. Firstly, generate the node admittance matrix which representing the distribution network information by using the line parameters and real-time topology of the distribution network; Secondly, establish the node voltage equation using the voltage data from the measuring points before and after the fault, then reconstruct the node positive sequence fault injection current by graph regularization and IRLS, select the optimal regular term parameters by the L-curve method; Finally, locate the fault intervals and even Accurate distance measurement of fault points according to the positive sequence fault injection current of the node after the effective processing. The simulation experiments of IEEE 33 node power distribution system show that installing only 7 measuring points, the proposed method can accurately locate the fault, and the fault location accuracy is less affected by the fault type and transition resistance, the method is simple in principle, and it has the anti-noise ability to meet the practical application.