Flood susceptibility mapping is an important method for flood research. In this paper, we combine a backpropagation neural network (BPNN) with a genetic quantum algorithm (GQA) for the first time to develop flood susceptibility mapping. The area on the Chinese side of the Tumen River Basin was selected as the research object. A set of flood conditioning factors was selected based on relevant literature and an actual situation and then validated using the chi-square test and correlation analysis. Different weights were assigned using stepwise weight assessment ratio analysis. Finally, modeling and flood susceptibility mapping using GQA-BPNN. As a reference, the same work was performed with both the pure BPNN and optimized BPNN using a genetic algorithm (GA). The results show that the area under the curve, root mean squared error, Nash-Sutcliffe coefficient and percentage of bias are significantly better for the GQA-BPNN than for the BPNN and GA-BPNN and that the flood sensitivity maps constructed by the GQA-BPNN have more flood points in high flood sensitivity areas. Therefore, the GQA-BPNN method can be considered an effective method for flood susceptibility mapping.