Sequential Recommendation (SR) characterizes evolving patterns of user behaviors by modeling how users transit among items. However, the short interaction sequences limit the performance of existing SR. To solve this problem, we focus on Cross-Domain Sequential Recommendation (CDSR) in this paper, which aims to leverage information from other domains to improve the sequential recommendation performance of a single domain. Solving CDSR is challenging. On the one hand, how to retain single domain preferences as well as integrate cross-domain influence remains an essential problem. On the other hand, the data sparsity problem cannot be totally solved by simply utilizing knowledge from other domains, due to the limited length of the merged sequences. To address the challenges, we propose DDGHM, a novel framework for the CDSR problem, which includes two main modules, i.e., dual dynamic graph modeling and hybrid metric training. The former captures intra-domain and inter-domain sequential transitions through dynamically constructing two-level graphs, i.e., the local graphs and the global graph, and incorporating them with a fuse attentive gating mechanism. The latter enhances user and item representations by employing hybrid metric learning, including collaborative metric for achieving alignment and contrastive metric for preserving uniformity, to further alleviate data sparsity issue and improve prediction accuracy. We conduct experiments on two benchmark datasets and the results demonstrate the effectiveness of DDHMG.