The edge effect is described as an unexpected bending angle variation along the scan line in the laser bending process. In this paper, an analytical model and finite element analysis of temperature fields and bending angles are used to obtain insight into the mechanism of edge effects in the laser bending process of DP980 high-strength steel. Based on the analysis of temperature distributions and influences of scanning velocity on edge effects, it is found that the edge effect of laser bending increases sharply with laser scanning velocity when the constant scanning velocity is smaller than 3 m/min. A varying velocity scanning strategy is proposed to reduce the edge effects of DP980 high-strength steel. By comparing the temperature distributions and bending angles between the varying velocity scanning and the constant one, it is confirmed that the relative bending angle variation in the varying velocity scanning strategy reduces by 54.1% compared to the constant one, which indicates that the varying velocity scanning strategy can significantly reduce the edge effect of the laser bending process. Simultaneously, the average bending angle of the steel sheet increases in the proposed new strategy, which indicates that forming efficiency is improved.