Deep-learning-based soft sensors have been extensively developed for predicting key quality or performance variables in industrial processes. However, most approaches assume that data are uniformly sampled while the multiple variables are often acquired at different rates in practical processes. This article designed a progressive transfer strategy, based on which a variational progressive-transfer network (VPTN) method is proposed for the soft sensor development of industrial multirate processes. In VPTN, the multirate data are first separated into multiple data chunks where the variables within each chunk are acquired at a uniform rate. Then, a variational multichunk data modeling framework is developed to model the multiple chunks in a unified fashion through deep variational structures. The base models, including the unsupervised ones with only partial process variables and the supervised soft sensor model share a similar network structure, such that the subsequent transfer strategy can be readily implemented. Finally, a progressive transfer learning strategy is designed to transfer the model parameters from the fastest sampled data chunk to the slowest one in a progressive manner. Thus, the knowledge from various data chunks can be sequentially explored and transferred to enhance the performance of the terminal soft sensor model. Case studies on both a debutanizer column dataset and a real coal mill dataset in a thermal power plant validate the performance of the proposed method.