This paper proposes a novel multi-source domain adaptation method for the health prediction in the absence of target batteries labels. First, a computationally efficient and effective source domain selection method is proposed. The proposed source domain selection method selects source domains with excellent transferability based on Euclidean distance and Sample Entropy thresholds, thereby improving the performance of multi-source domain adaptation. Second, improved maximum mean discrepancy is proposed to guide the representation alignment. Compared with the original maximum mean discrepancy, it matches the source data with the target data in the order of aging, thus preserving the time order of the distribution. Third, we develop a multi-source domain adaptation network that contains a domain-invariant feature generator and several domain-specific feature generators and estimators. Two out of 12 datasets are used as target LIBs to evaluate the performance of the proposed method. The mean absolute error of the proposed method on these two datasets is only 0.671% and 0.868%, respectively. While the maximum error of MDA-IM-GC on both datasets does not exceed 5.2%. The experiment results indicate that the proposed network provides impressive accuracy with only 1/10 of unlabeled target historical data accessible and outperforms the single-source domain adaptation approach.