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For both driving safety and efficiency, automated vehicles should be able to predict the behavior of surrounding traffic participants in a complex dynamic environment. To accomplish such a task, trajectory prediction is the key. Although many researchers have been engaged in this topic, it is still challenging. One of the important and inherent factors is the multi-modality of vehicle motion. Because of the disparate driving behaviors under the same condition, the prediction of vehicle trajectory should also be multi-modal. At present, related researches have more or less shortcomings for multi-modal trajectory prediction, such as requiring explicit modal labels or multiple forward propagation caused by sampling. In this work, we focus on overcoming these issues by pointing out the dual-levels of multi-modal characteristics in vehicle motion and proposing the dual-level stochastic multiple choice learning method (named as DsMCL, for short). This method does not require modal labels and can implement a comprehensive probabilistic multi-modal trajectory prediction by a single forward propagation. By experiments on the NGSIM and HighD datasets, our method has proven significant improvement on several trajectory prediction frameworks and achieves state-of-the-art performance.