During travel of a vehicle, an apparatus acquires vehicle velocity information detected by a vehicle velocity sensor and a reference accelerator opening degree and an estimated gear position from a reference accelerator opening degree table indicative of relationship between vehicle velocities and accelerator opening degrees during travel of the vehicle at cruising velocity. The apparatus also acquires an estimated number of prime mover rotations at the vehicle velocity from a vehicle-velocity vs. number-of-prime-mover-rotation correlation table, and then calculates a difference between the estimated number of prime mover rotations and an actual number of prime mover rotations detected by a number-of-prime-mover-rotation sensor. Further, a value, obtained by multiplying the calculated difference by a compensating coefficient determined in accordance with characteristics specific to the vehicle, is added to the reference accelerator opening degree, to thereby calculate an estimated accelerator opening degree.