The invention relates to a least square positioning algorithm for distribution network faults. The method comprises steps of S1: setting a plurality of fault detection points on a distribution network line and synchronously acquiring current and voltage waveforms; S2: selecting any line having faults at two ends, and correcting parameters per line unit length; S3: performing Karrenbauer transform three-phase decoupling on the current and voltage waveforms of the fault detection points; S4: multiplying the corrected parameters per line unit length by the line length to get corrected parameters of the line; S5: combining the corrected parameters of the line, and establishing the voltage and current equations of the fault point and each fault detection point; and S6: using the least square algorithm to solve the system of equations to obtain the best estimation value of the fault distance. The algorithm utilizes the voltage and current waveforms before the fault occurs to correct the line parameters. After the fault occurs, the voltage and current equations between the fault point and the fault detection point are established through the fault analysis method according to the line parameters to realize the precise fault location.