The Remaining Useful Life (RUL) of lithium batteries is vital for maintaining and safely operating the batteries, making precise RUL predictions highly significant. This paper introduces a method for predicting the RUL of lithium-ion batteries, utilizing a kernel adaptive filtering algorithm integrated with Deep Belief Networks (DBN). The method constructs a novel prediction model based on the Fixed-Budget Kernel Recursive Least Squares (FB-KRLS) algorithm. In this approach, the DBN extracts features from the original lithium battery data to reduce data complexity. The Square-root Cubature Kalman Filter (SCKF) is integrated with the FB-KRLS algorithm, employing a dual al-ternating learning strategy to improve the model's nonlinear fitting performance. The model was validated using NASA's lithium battery data, showing that the minimum val-ues for the MAPE, RMSE and MAE were 0.102%, 0.0016 and 0.0014, respectively. Therefore, the proposed method demonstrates potential for application in predicting the RUL of lithium-ion batteries.