The state of health (SOH) prediction of lithium-ion batteries (LIBs) is of crucial importance for the normal operation of the battery system. In this paper, a new method for cycle life and full life cycle capacity prediction is proposed, which combines the early discharge characteristics with the neural Gaussian process (NGP) model. The cycle data sets of commercial LiFePO4(LFP)/graphite cells generated under different operating conditions are analyzed, and the power characteristic P is extracted from the voltage and current curves of the early cycles. A Pearson correlation analysis shows that there is a strong correlation between P and cycle life. Our model achieves 8.8% test error for predicting cycle life using degradation data for the 20th to 110th cycles. Based on the predicted cycle life, capacity degradation curves for the whole life cycle of the cells are predicted. In addition, the NGP method, combined with power characteristics, is compared with other classical methods for predicting the remaining useful life (RUL) of LIBs. The results demonstrate that the proposed prediction method of cycle life and capacity has better battery life and capacity prediction. This work highlights the use of early discharge characteristics to predict battery performance, and shows the application prospect in accelerating the development of electrode materials and optimizing battery management systems (BMS).