The double stack car carriers transportation problem of vehicle logistics belongs to a kind of combinatorial optimization problem that needs to consider the vehicle filling problem(VFP) and vehicle routing problem(VRP), which is called vehicle filling and routing problem(VFRP). Because the complexity of the VFP and VRP is NPC(non-deterministic polynomial complete problem), and the objective functions and constraints of models of the VFRP and other combinatorial optimization problems often have nonconvex structure, the linearization, the design of accurate algorithms and the improvement of solution efficiency are always the difficulties in this field. Therefore, a VFRP model of double stack car carriers transportation is constructed, aiming at the lowest cost of car carriers transportation. On this basis, two linearization methods are proposed, and an improved branch-and-price algorithm is designed to solve the problem: on the basis of branch-and-price algorithm, a branch strategy of combining the most-infeasible-branching strategy and the strong-branching strategy, and a dimension reduction method of reducing the feasible region's dimension, are proposed to accelerate convergence. Finally, examples with actual data are designed, which verify the effectiveness of the model and the algorithm.