We investigate the origin of the high orbital eccentricity and inclination of present asteroids. The relative velocity between asteroids corresponding to the observed high eccentricity and inclination is ∼5 km/sec, which is much larger than their surface escape velocity. Thus collisions result in disruption rather than accretion. It is important to clarify when and how their eccentricity and inclination were pumped up, in order to know the environment of asteroidal disruption. The origin of high eccentricity and especially that of inclination have not been well understood yet. We propose sweeping secular resonances due to the gravitational potential change associated with the depletion of the protoplanetary nebula as the excitation mechanism of eccentricity and inclination. We calculated magnitudes of excited eccentricity and inclination through three-dimensional orbital integration. We found that both eccentricity and inclination are excited enough if the protoplanetary nebula is depleted from inside to outside in the region between 5 AU to 10 AU on a timescale ≳5 × 105 years. We found that the secular resonances sweep the asteroid belt after the nebula gas is removed from there. Then the asteroidal motion is not affected by gas drag significantly. High velocity collisions between asteroids would occur in a gas-free environment.