Due to operating condition drift, environmental changes, and system oscillations, industrial processes often exhibit nonstationary characteristics that involve both stable long-term trend and fluctuant short-term dynamics. In this article, a novel multiscale gated structure model (MGSM) is proposed for nonstationary process soft sensing, which includes long-term memory chain (stable and low frequency) and short-term dynamic chain (respond to fluctuations). The information decomposed from input data is introduced into the MGSM to learn long-term dependency relationships and dynamic behavior in the nonstationary process. In addition, a novel two-dimensional random missing function is designed to handle randomly missing data, which fully considers the data missing in variable-wise and time-wise dimensions. The proposed model is further constructed for the soft sensing of nonstationary processes with random missing data. Finally, application studies to the Tennessee Eastman process and a thermal power generating process show that the proposed method has significant advantages in the quality prediction of nonstationary process.