A task allocation method based on the fusion genetic slime mould algorithm (FGSMA) was proposed aiming at the problem of collaborative multi-drone task allocation in a known battlefield environment. The objective function for multi-drone collaborative task allocation was constructed by considering the constraints of individual drones, the overall benefit and loss of the drone group, as well as the task requirements. The genetic iteration and slime mould exploration behaviors were improved in order to address the issues of genetic algorithms’ tendency to fall into local optima and the slow convergence of slime mould algorithms. The discrete slime mould algorithm was introduced into the genetic algorithm to enhance the search capability of the fused algorithm. A disturbance operation was added to the population iteration in order to improve the solution accuracy. Allocation experiments and path demonstrations were conducted in a known environment, and comparisons with other algorithms were conducted. Results show that the proposed fusion algorithm can obtain a task allocation scheme with a higher objective function value.