Research on fault diagnosis and positioning of the distribution network (DN) has always been an important research direction related to power supply safety performance. The back propagation neural network (BPNN) is a commonly used intelligent algorithm for fault location research in the DN. To improve the accuracy of dual fault diagnosis in the DN, this study optimizes BPNN by combining the genetic algorithm (GA) and cloud theory. The two types of BPNN before and after optimization are used for single fault and dual fault diagnosis of the DN, respectively. The experimental results show that the optimized BPNN has certain effectiveness and stability. The optimized BPNN requires 25.65 ms of runtime and 365 simulation steps. And in diagnosis and positioning of dual faults, the optimized BPNN exhibits a higher fault diagnosis rate, with an accuracy of 89%. In comparison to ROC curves, the optimized BPNN has a larger area under the curve and its curve is smoother. The results confirm that the optimized BPNN has high efficiency and accuracy.