An improved genetic-simulated annealing algorithm was proposed for the logistics task allocation problem of UAVs in cities. Firstly, considering the performance limitations of heterogeneous UAVs, hard constraints were established and task time windows were set as soft constraints to construct a drone task allocation model with the minimum total cost. Secondly, the adaptive crossover mutation rate was used to improve the genetic algorithm, and an elite retention strategy was adopted to achieve a dynamic balance between the breadth and accuracy of the search. To avoid genetic algorithm getting stuck in local optima, simulated annealing algorithm was introduced, and an adaptive temperature decay function was used to improve the quality of the solution. In the improved fusion algorithm, partial offspring were selected through random probability for local optimization, and the frequency of simulated annealing was dynamically adjusted to find a balance between global search and local optimization. The simulation experiment results show that the proposed IGASA (improved genetic-simulated annealing algorithm) reduces the total cost by 9.5% and 7.4% respectively compared to traditional genetic algorithms and simulated annealing algorithms.