Weather radar, as a crucial component of remote sensing data, plays a vital role in convective weather forecasting through radar echo extrapolation techniques. To address the limitations of existing deep learning methods in radar echo extrapolation, this paper proposes a radar echo extrapolation model based on video vision transformer and spatiotemporal sparse attention (ViViT-Prob). The model takes historical sequences as input and initially maps them into a fixed-dimensional vector space through 3D convolutional patch encoding. Subsequently, a multi-head spatiotemporal fusion module with sparse attention encodes these vectors, effectively capturing spatiotemporal relationships between different regions in the sequences. The sparse constraint enables better utilization of data structural information, enhanced focus on critical regions, and reduced computational complexity. Finally, a parallel output decoder generates all time step predictions simultaneously, then maps back to the prediction space through a deconvolution module to reconstruct high-resolution images. Our experimental results on the Moving MNIST and real radar echo dataset demonstrate that the proposed model achieves superior performance in spatiotemporal sequence prediction and improves the prediction accuracy while maintaining structural consistency in radar echo extrapolation tasks, providing an effective solution for short-term precipitation forecasting.