High-rise building machines (HBMs) play a critical role in the successful construction of super-high skyscrapers, providing essential support and ensuring safety. The HBM’s climbing system relies on a jacking mechanism consisting of several independent jacking cylinders. A reliable control system is imperative to maintain the smooth posture of the construction steel platform (SP) under the action of the jacking mechanism. Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Temporal Convolutional Network (TCN) are three multivariate time series (MTS) neural network models that are used in this study to predict the posture of HBMs. The models take pressure and stroke measurements from the jacking cylinders as inputs, and their outputs determine the levelness of the SP and the posture of the HBM at various climbing stages. The development and training of these neural networks are based on historical on-site data, with the predictions subjected to thorough comparative analysis. The proposed LSTM and GRU prediction models have similar performances in the prediction process of HBM posture, with medians R2 of 0.903 and 0.871, respectively. However, the median MAE of the GRU prediction model is more petite at 0.4, which exhibits stronger robustness. Additionally, sensitivity analysis showed that the change in the levelness of the position of the SP portion of the HBM exhibited high sensitivity to the stroke and pressure of the jacking cylinder, which clarified the position of the cylinder for adjusting the posture of the HBM. The results show that the MTS neural network-based prediction model can change the HBM posture and improve work stability by adjusting the jacking cylinder pressure value of the HBM.