Accurate and reliable prediction of the battery capacity degradation is vital for predictive health management. This paper proposes a novel framework to improve the accuracy and reliability of battery health prognostic. Firstly, sequential information-ensembled health indicators, which have high correlations with battery capacity and lifetime, are proposed based on partial voltage and capacity sequences. Then, the Gaussian mixture model is adopted for lifetime clustering to verify the effectiveness of the proposed health indicators and an automatic reference batteries selection method is proposed to find out the most relative candidates for degradation base model training. A long short-term memory network with probabilistic regression is leveraged for battery health prognostic, which provides the predicted mean value and confidence interval via Bayesian inference. Finally, the model migration is presented to further improve the accuracy and reliability, with only a few checkpoints used for re-training. The proposed framework for battery health prognostic is validated against four battery datasets, showing high accuracy and reliability. Specifically, the root mean square error and mean absolute error of health prognostic on all the battery cells in four battery dataset can be within 2% and 1.5%, respectively. The mean relative reductions of the above two errors reach 43.7% and 45.3% respectively compared to the conventional method.