Continuous detection of space precession cone targets using broadband radars can generate high-resolution range profile (HRRP) sequences. The HRRP sequences contain information such as spatial geometric information and precession laws of space cone targets, which are applicable to target association, tracking and classification. Therefore, it is of great significance to perform HRRP sequence prediction for spatial precession cone targets. The ConvLSTM network effectively combines the characteristics of CNN and LSTM, which can fully mine spatial and temporal information of HRRP sequences to achieve prediction of HRRP. This article establishes a HRRP sequence dataset based on the precession model of spatial cone targets, which incorporates different parameters such as size, motion speed and motion direction, and uses this dataset to design and implement a ConvLSTM network model suitable for HRRP prediction for spatial precession cone targets according to HRRP characteristics. In order to validate the predictions by the ConvLSTM network designed in this paper, the ConvLSTM network is compared with the two-dimensional convolutional neural network mode. Simulation and experimental results show that ConvLSTM network is in good agreement with HRRP calculated using physical optics method, and is more accurate than predictions of 2D convolutionneural network. The Pearson correlation coefficient is as high as 0.973 1, and average absolute error reaches 0.033 4. The ConvLSTM network model can effectively extract temporal and spatial features of HRRP sequences to achieve high-precision prediction of HRRP sequences.