Abstract: The fuel consumption of ground vehicles in accelerating scenarios is significantly affected by how they are driven. This paper quantitatively studies the fuel optimal accelerating strategies for vehicles with discontinuous gear ratio under the optimal control framework. The identification of economical accelerating strategy is converted into a Bolza-typed optimal control problem (OCP), in which an equivalent fuel consumption index is proposed to eliminate the difference of accelerating distances. The converted OCP has discontinuous input, i.e. gear ratio of transmission, and nonlinear cost function and plant model, which naturally casts in the mixed-integer OCP. Considering the gear shifting rules of mechanical transmission, we transform the discontinuous OCP into multiple but interconnected continuous problems. The multiple-phase knotting technology combining Legendre pseudospectral discretization is used to obtain the optimal numerical solutions to gear position, gear shifting time, and engine torque. The mechanism of the fuel optimal accelerating strategy is analyzed, and the practical rules of gear shifting and acceleration selection are also summarized. The fuel benefit of the economical accelerating strategy is validated by simulations.