As the demand for efficient parcel delivery continues to grow in the logistics industry, optimizing multi-robot task assignment has become crucial for enhancing overall delivery performance. This paper addresses the precedence-constrained multi-truck multi-drone package delivery task assignment problem, where each truck coordinates with a drone to serve multiple dispersed customers under precedence constraints that specify the required order of service. While trucks deliver packages to designated customers, drones can simultaneously serve other customers, subject to their limited flight endurance and payload capacity. To tackle this challenge, a three-phase heuristic algorithm is proposed to minimize the total delivery time required to serve the last customer while ensuring all precedence constraints are satisfied. In the first phase, an extended minimum marginal cost algorithm is applied to quickly construct truck-only routes that comply with precedence constraints. In the second phase, a splitting algorithm combined with an endurance checking procedure is employed to generate hybrid truck–drone routes considering drone limitations. In the final phase, a variable neighborhood descent approach is introduced to further improve the solution by strategically perturbing the truck-only routes. Extensive simulations and experiments demonstrate that the proposed three-phase heuristic algorithm consistently achieves higher-quality solutions with reduced computation time compared with the widely used adaptive large neighborhood search method.