In a speed change apparatus for a vehicle, a controller stores as a clutch-disengaging shift spindle angle θ1 a position at which a clutch is disengaged when a shift spindle is rotated in a first direction. The controller controls the shift spindle by a first step W1 of rotating the shift spindle in the first direction until a disengaging-side target angle Ta1 is reached; a second step W2 of returning the shift spindle in a second direction opposite to the first direction; and a third step W3 of rotating the shift spindle in the first direction up to the clutch-disengaging shift spindle angle θ1 and thereafter rotating the shift spindle in the second direction to return the shift spindle, upon detection of an output from a drum angle sensor, the output corresponding to shallow engagement of dog teeth.