Accurate motion prediction of pedestrians, cyclists, and other surrounding vehicles (all called agents) is very important for autonomous driving. Most existing works capture map information through an one-stage interaction with map by vector-based attention, to provide map constraints for social interaction and multi-modal differentiation. However, these methods have to encode all required map rules into the focal agent's feature, so as to retain all possible intentions' paths while at the meantime to adapt to potential social interaction. In this work, a progressive interaction network is proposed to enable the agent's feature to progressively focus on relevant maps, in order to better learn agents' feature representation capturing the relevant map constraints. The network progressively encode the complex influence of map constraints into the agent's feature through graph convolutions at the following three stages: after historical trajectory encoder, after social interaction, and after multi-modal differentiation. In addition, a weight allocation mechanism is proposed for multi-modal training, so that each mode can obtain learning opportunities from a single-mode ground truth. Experiments have validated the superiority of progressive interactions to the existing one-stage interaction, and demonstrate the effectiveness of each component. Encouraging results were obtained in the challenging benchmarks.