This paper investigates the downlink scheduling for relay-aided high-mobility vehicular networks, where the vehicles with good vehicle-to-infrastructure (V2I) links are employed as cooperative relay nodes to help the ones with poor V2I links forward information via vehicle-to-vehicle (V2V) links. In existing works, instantaneous achievable information rate was widely adopted to perform the link scheduling, but it is not efficient for vehicular networks, especially for high-mobility scenarios. Different from them, in this paper, we introduce the mobile service to describe the mobile link capacity of vehicular networks and then we propose a mobile service based relaying scheduling (MSRS) for high mobility vehicular networks. In order to explore the system information transmission performance limit, we formulate an optimization problem to maximize the mobile service amount of MSRS by jointly scheduling the V2I and V2V links. Since it is a combinational optimization problem which is too complex to solve, we design an efficient algorithm with low-complexity for it, where Sort-then-Select, Hungarian algorithm and Bisection search are employed. Simulation results demonstrate that our proposed MSRS is able to achieve the optimal results with an optimal approximation ratio larger than 96.5%. It is also shown that our proposed MSRS is much more efficient for high-mobility vehicular systems, which can improve the system average throughput with increment of 3.63% compared with existing instantaneous achievable information rate based scheduling method, and with 15% increment compared with traditional non-cooperation scheduling method, respectively.