In recent years, the substantial growth in satellite data transmission tasks and volume, coupled with the limited availability of ground station hardware resources, has exacerbated conflicts among missions and rendered traditional scheduling algorithms inadequate. To address this challenge, this paper introduces an improved tabu genetic hybrid algorithm (ITGA) integrated with heuristic rules for the first time. Firstly, a constraint satisfaction model for satellite data transmission tasks is established, considering multiple factors such as task execution windows, satellite–ground visibility, and ground station capabilities. Leveraging heuristic rules, an initial population of high-fitness chromosomes is selected for iterative refinement. Secondly, the proposed hybrid algorithm iteratively evolves this population towards optimal solutions. Finally, the scheduling plan with the highest fitness value is selected as the best strategy. Comparative simulation experimental results demonstrate that, across four distinct scenarios, our algorithm achieves improvements in the average task success rate ranging from 1.5% to 19.8% compared to alternative methods. Moreover, it reduces the average algorithm execution time by 0.5 s to 28.46 s and enhances algorithm stability by 0.8% to 27.7%. This research contributes a novel approach to the efficient scheduling of satellite data transmission tasks.