Brassica napus is one of the most important oil crops in China. Rapeseed production has a pivotal effect on the edible oil supply security and the national economy in our country. With the global climate change, drought has become a main restriction factor for agricultural development, and brought heavy losses to rapeseed production. Therefore, investigating the mechanism of rape response to drought stress and improving the drought resistance of rapeseed possesses great significance. In this study, the drought resistance of three offspring lines of intergeneric somatic hybrids between Brassica napus and Sinapis alba and B. napus cv. Y6 (Yangyou 6) during seed germination stage were evaluated. The morphological, physiological, biochemical changes and the transcript abundance of a series of antioxidant enzyme encoding genes were examined. Under drought stress simulated by 15% PEG (polyethylene glycol) treatment, compared with the control (Y6), the root and shoot development of the hybrid offspring materials were less inhibited. The MDA (malondialdehyde) content of the hybrid offspring materials was lower than that of Y6, and the ROS (reactive oxygen species) accumulation in the hybrid offspring materials was higher than that in Y6. Moreover, the transcript level of some antioxidant enzyme encoding genes was obviously higher in the hybrid offspring materials than that in Y6. Our results indicated that the hybrid offspring materials may derive stronger drought resistance from the parent-Sinapis alba.