The present study focuses on the application of stochastic modeling technique in analyzing the remaining useful life prediction of lithium battery. For this, the Box-Jenkins ARIMA model has been used for simulating the lithium battery degradation process. The lithium battery dataset has been collected from NASA PCoE. ADF unit root test and difference method are used to smooth the original data of lithium battery capacity. The parameters are estimated by analyzing autocorrelation function and partial autocorrelation function. Several ARIMA models have been generated and their validation has been verified by assessing various estimation parameters. According to AIC, SC criteria and normalized BIC, the optimal prediction model is selected. After rigorous evaluation of the selected models, the ARIMA(2,1,2)is indentified as the best fit model. Satisfactory results have been obtained with the selected ARIMA models, indicating that the ARIMA model is highly accurate and feasible in the short term.