The S-wave velocity () is a fundamental parameter in geophysical analysis, prestack seismic inversion, and reservoir prediction. For various reasons, the availability of directly measured values of is low, especially in old wells. Therefore, indirect estimations of data on the basis of available reservoir information are important, and the development of a high-efficiency and low-cost prediction method is necessary. We have developed a novel prediction method that combines the convolutional neural network (CNN) and the gated recurrent unit (GRU) algorithms, based on a deep convolutional GRU (DCGRU) approach. More specifically, a CNN structure is used to identify and memorize the complex relationship between and well-log data, whereas a GRU network is introduced to extract key features of the data series in the depth direction. Owing to its structure, the DCGRU approach can seamlessly account for data trends with depth, local correlations across data series, and the actual depth accumulation effect. This approach is tested on data sets from an actual reservoir; it provides more reliable and accurate predictions not only compared with empirical models but also compared with the CNN and GRU algorithms applied separately. Our approach has potential for accurately estimating from log data.