Extrapolation technique of weather radar echo possesses a widely application prospects in short-term nowcast. The traditional methods of radar echo extrapolation are difficult to obtain long limitation period and have low utilization rate of radar data. This problem is researched from deep learning perspective in this paper, and a new model named Dynamic Convolutional Neural Network based on Input (DCNN-I) was proposed. According to the strong correlation between weather radar echo images at adjacent times, dynamic sub-network and probability prediction layer were added, and a function was created that maped the convolution kernels to the input, through which the convolution kernels could be updated based on the input weather radar echo images during the testing. In the experiments of radar data from Nanjing, Hangzhuo and Xiamen, this method achieved higher accuracy of prediction images compared with traditional methods, and extended the limitation period of exploration effectively.