Consistence of lithium-ion power battery significantly affects the life and safety of battery modules and packs. To improve the consistence, battery grouping is employed, assembling batteries with similar electrochemical characteristics to make up modules and packs. Therefore, grouping process boils down to unsupervised clustering problem. Current used grouping approaches include two aspects, static characteristics based and dynamic based. However, there are three problems. First, the common problem is under utilization of multi-source data. Second, for the static characteristics based, there is grouping failure over time. Third, for the dynamic characteristics based, there is high computational complexity. To solve these problems, we propose a distributed multisource data fusion based battery grouping approach. The proposed approach designs an effective network structure for multisource data fusing and feature extracting from both static and dynamic multisource data. We apply our approach on real battery modules and record state of health (SOH) during charging-discharging cycles. Experiments indicate that the proposed approach can increase SOH of modules by 3.89% and reduce the inconsistence by 68.4%. Meanwhile, with the distributed deployment the time cost is reduced by 87.9% than the centralized scheme.