To optimise the trucking problem with time windows, a multi-objective mathematical programming model was established for separated vehicle scheduling. To compute Pareto solutions, a phased optimal algorithm based on hybrid quantum evolution was put forward. To enhance the convergence rate, a greedy repair operator was designed. To avoid premature convergence, a neighbourhood search based on node switching was performed. To maintain the dispersion of the Pareto solutions, an adaptive grid operator was designed. The effectiveness of the proposed method compared to previous scheduling modes and other algorithms was verified experimentally. For the same transport capacity, the vehicle scheduling method based on a quantum evolutionary algorithm can greatly reduce both the number of vehicles and cost.