As a sign of porosity and permeability, spontaneous-potential (SP) well logging plays an important role in reservoir division and evaluation. Complete and effective SP logging is helpful to obtain high resolution sandstone-mudstone section and is a reliable basis for oil-gas reservoir interpretation. However, in the actual mining process, distortion or incomplete of SP logging commonly exists due to instrument damage, borehole collapse and other reasons. Moreover, SP re-logging is expensive and difficult to implement. In this paper, we develop an alternative SP logging reconstruction technique based on Bidirectional gated recurrent unit (BiGRU) neural network. By considering the relationship between current logging data and historical and future logging data, and the nonlinear mapping relationship between different logging curves, the intelligent and effective completion of missing logging is realized. Extensive experiments are carried out in the Jiyang Depression, Shengli Oilfield to verify the effectiveness of the proposed method. The results show that BiGRU has higher reconstruction accuracy than gated recurrent unit (GRU), support vector regression (SVR) and linear regression (LR), which provides a new development direction for logging reconstruction.