As an automatic and efficient delivery approach, the unmanned aerial vehicle (UAV) has received much attention in the field of electronic commerce and urban logistics for its natural ability to avoid traffic congestion. Regarding the arrangement of UAV delivery paths as a multi-objective path planning problem, we propose a novel genetic method based on the Non-Dominant Sorting Genetic Algorithm II (NSGA-II) with constraints to optimize the multi-UAV path planning problem, which is to minimize the total cost while maximizing customer satisfaction. In this algorithm, decision vectors are represented as 1-dimensional chromosomes, and two specialized variation operators are employed. These designs, as well as the properties of NSGA-II, enable us to find more non-crowding Pareto optimal solutions with less calculation. In a case study on part of the Solomon dataset, this algorithm found three sparsely distributed non-dominant solutions in one Pareto frontier within a relatively small population size and a short time.