Accurate trajectory prediction of surrounding vehicles is vital for automated vehicles to achieve high-level driving safety in complex situations. However, most state-of-the-art approaches for multi-vehicle trajectory prediction ignore vehicle motion uncertainty caused by different driving styles. Moreover, the interrelationship between the vehicle and the environment is seldom considered. To address the above problems, this paper proposes a driving risk map-integrated deep learning (DRM-DL) method for interactive trajectory prediction of surrounding vehicles, which comprehensively considers the motion uncertainty, trajectory intention uncertainty and interactions among vehicles, lane lines and road boundaries. Specifically, we adopt a conditional variational autoencoder (CVAE) to generate the candidate trajectories, in which the motion uncertainty is considered using a conditional Gaussian distribution. Furthermore, a driving risk map is constructed to realize a unified and interpretable representation of vehicle-vehicle and vehicle-environment interactions. The probability of each candidate trajectory is assigned using a trajectory probability model and a random selection is adopted to select a guided trajectory, which simulates the driver’s trajectory intention uncertainty. Finally, a relearning module is designed to obtain the precise trajectory prediction for surrounding vehicles. The proposed method is evaluated on the HighD dataset, and the results demonstrate a more accurate and reliable trajectory prediction for surrounding vehicles compared with state-of-the-art methods.