A first signal is obtained by detecting speed of wheels of a vehicle to indicate the wheel speed. On the other hand, a second signal is obtained by detecting longitudinal acceleration to directly indicate longitudinal acceleration of the vehicle. A third signal indicating the change rate of the wheel speed is obtained by differentiating the first signal by time. The third signal is sensitive to a small convex or concave of the road surface but not sensitive to a longitudinal inclination of the road surface. The second signal is not sensitive to a small convex or concave of the road surface but is sensitive to a longitudinal inclination of the road surface. Then, a fourth signal is obtained from the second signal by filtering low frequency components off therefrom, while a fifth signal is obtained from the third signal by filtering high frequency components off therefrom. Then, a final longitudinal acceleration signal is obtained by composing the fourth and fifth signals together. It will be desirable that a cutoff frequency of the low pass filtering is lowered when a brake locking has occurred.