The Length of Day (LOD) and the Universal Time (UT1) play crucial roles in satellite positioning, deep space exploration, and related fields. The primary method for predicting LOD and UT1 is least squares fitting combined with autoregressive (AR) models. Polynomial Curve Fitting (PCF) has greater accuracy in capturing long-term trends compared to standard least squares fitting. In this study, PCF combined with Weighted Least Squares (WLS) is employed to fit and extrapolate the periodic and trend components of the LOD series after removing tidal influences. Additionally, considering the time-varying characteristics of the LOD series, a Long Short-Term Memory (LSTM) network is utilized to predict the residuals derived from the fitting process. The 14 C04 LOD series released by the International Earth Rotation and Reference System Service (IERS) is used as the base series, with 70 LOD and UT1-UTC prediction experiments conducted during the period from 1 September 2021–31 December 2022. The results indicate that the PCF+WLS+LSTM method is well-suited for medium- and long-term (90–360 days) prediction of the LOD and UT1-UTC. Significant improvements in prediction accuracy were obtained for periods ranging from 90–360 days, particularly beyond 150 days, where the average accuracy improved by over 20% compared to IERS Bulletin A. Specifically, the largest prediction accuracy increase for LOD and UT1-UTC was 49.5% and 59.2%, respectively.