Battery capacity is an important metric for evaluating and predicting the health status of lithium-ion batteries. In order to determine the answer, the battery’s capacity must be, with some difficulty, directly measured online with existing methods. This paper proposes a multi-dimensional health indicator (HI) battery state of health (SOH) prediction method involving the analysis of the battery equivalent circuit model and constant current discharge characteristic curve. The values of polarization resistance, polarization capacitance, and initial discharge resistance are identified as the health indicators reflective of the battery’s state of health. Moreover, the retention strategy genetic algorithm (e-GA) selects the optimal voltage drop segment, and the corresponding equal voltage drop discharge time is also used as a health indicator. Based on the above health indicator selection strategy, a battery SOH prediction model based on particle swarm optimization (PSO) and LSTM neural network is constructed, and its accuracy is validated. The experimental results demonstrate that the suggested strategy is accurate and generalizable. Compared with the prediction model with single health indicator input, the accuracy is increased by 0.79%.