An extension/retraction cylinder stops or starts tilting the platform of the stair-climbing wheelchair carrier based on a detection signal from an inclination sensor provided in the crawler drive unit. When the crawler drive unit is detected to be not tilted, the tilting motion of the platform is stopped at an intermediate angle (e.g. 20.degree.) of a maximum preset angle (e.g. 40.degree.). When the crawler drive unit is detected to be tilted, the platform is tilted up to the maximum preset angle, and as soon as the crawler drive unit is detected not to be tilted after tilting, the platform is driven so as to decrease its inclination angle relative to the crawler drive unit. Thus, a comfortable and usable stair-climbing wheelchair carrier can be provided.