Multi-modal trajectory prediction (MTP) has become the research trend in the field of autonomous driving, as it provides multiple plausible trajectories. However, related works lack attention to the temporal dependence of historical features and inherent association between multiple trajectory modes, which may lead to large deviations. To address these critical limitations, we propose a multi-modal trajectory prediction network that integrates historical motion and spatio-temporal interaction (MTPN-IMI). In MTPN-IMI, a local spatio-temporal graph (LSTG) is constructed to model local agent-agent interaction. Furthermore, a Causal Convolution Module (CCM) and a Causal Self-Attention Module (CSAM) are introduced to focus on local and global temporal dependence in historical motion feature and local agent-agent interaction feature. Moreover, a Cross Attention Module (CAM) is utilized to capture the inherent association between multiple modes. Experiments show that our model outperforms related models on Argoverse1.1 validation set, achieving superior prediction accuracy.