High-Resolution Range Profile (HRRP) sequence has attracted academic attentions in the field of radar automatic target recognition (RATR) owing to its abundant spatial-temporal correlation between adjacent samples. However, it is difficult in the working state of radar to obtain complete HRRP sequence samples due to various internal and external factors such as ground clutter and systematic error, which poses an enormous challenge to radar target recognition. Therefore, it is crucial to repair the missing HRRPs based on the adjacent samples in the previous frames. In this paper, we discuss the extrapolate method of incomplete samples and propose an improved neural network algorithm named as Vanishing Gradient Mitigation Recurrent Neural Network (VGM-RNN). The lost samples in the sequence can be extrapolated by VGM-RNN, and the problem of vanishing gradient which is possessed in classical RNN can be effectively mitigated. The proposed method in this paper can be divided into two parts, as sample extrapolation and sequence recognition, in which sample extrapolation is the core method. Experimental results on Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset show that our proposed model exhibits higher accuracy and efficiency, as well as excellent anti-noise performance, compared with traditional methods. It is suggested that our proposed model can be effectively applied to radar system.