The Gravity Recovery and Climate Experiment (GRACE) satellite mission, spanning from 2002 to 2017, has provided a valuable dataset for monitoring variations in Earth's gravity field, enabling diverse applications in geophysics and hydrology. The mission was followed by GRACE Follow-On in 2018, continuing data collection efforts. The monthly Earth gravity field, derived from the integration different instruments onboard satellites, has shown inconsistencies due to various factors, including gaps in observations for certain instruments since the beginning of the GRACE mission. With over two decades of GRACE and GRACE Follow-On data now available, this paper proposes an approach to fill the data gaps and forecast GRACE accelerometer data. Specifically, we focus on accelerometer data and employ Long Short-Term Memory (LSTM) networks to train a model capable of predicting accelerometer data for all three axes. In this study, we describe the methodology used to preprocess the accelerometer data, prepare it for LSTM training, and evaluate the model's performance. Through experimentation and validation, we assess the model's accuracy and its ability to predict accelerometer data for the three axes. Our results demonstrate the effectiveness of the LSTM forecasting model in filling gaps and forecasting GRACE accelerometer data.