The state of charge (SOC) of an electric vehicle is very important for predicting the remaining battery level and safely protecting the battery from over-discharge and overcharge conditions. In this regard, a neural network (NN) algorithm using backpropagation (BP) has been proposed to accurately estimate the SOC of a battery. Lithium polymer batteries have a nonlinear relationship between their estimated SOC and the current, voltage, and temperature. In this study, a lithium polymer battery with a capacity of 3.7 V/16 Ah was applied. A charge/discharge experiment was performed under constant current and temperature conditions at a discharge rate of 0.5 C. The experimental data were used to train a backpropagation neural network (BPNN) that was used to predict the SOC under charging conditions and the depth of dispatch (DOD) performance under discharge conditions. As a result of the experiment, the error of the proposed BPNN model was found to be 0.22% of the mean absolute error in the discharge DOD and 0.19% of the mean absolute error in the charging SOC at 10, 50, 100, and 150 cycles. Therefore, the high performance of the SOC learning model of the designed BP algorithm was confirmed.