Well logging is a common method that is used to obtain the rock properties of a formation. It is relatively frequent, however, that log information is incomplete due to cost limitations or borehole problems. Existing models predict missing well logs from a fixed combination of other available well logs. However, the missing well logs vary from well to well. We have proposed using a gated graph neural network (GNN) to handle the missing values in well-log curves. It takes sequential data, predicting each missing measurement in the data not only using other available variables measured at the same depth but also available measurements of neighboring observations. Meanwhile, the missing well logs and available well logs could be any possible combinations as long as they are mutually exclusive. This approach has two advantages: (1) the gated GNN does not need to build a specific model for each missing measurement or from every possible combination of available measurements and (2) it can be integrated into the training process of the following predictive model to perform classification tasks. We evaluate the gated GNN model along with two other models: the GRAPE model and the multiple imputation by chained equations (MICE)-gated recurrent unit (GRU) model, on a data set from the North Sea to perform a missing feature imputation task and a lithofacies identification task. The GRAPE model also is a graph-based model, and it predicts values for each missing measurement from available variables measured at the same depth. The MICE-GRU model is a combination of the MICE algorithm and GRU, which handles the feature imputation procedure and the lithofacies identification procedure separately. Our experiments find that the gated GNN model outperforms the MICE algorithm and the GRAPE model on the missing feature imputation task. For the lithofacies identification task, the gated GNN model also provides comparable results to the MICE-GRU model, and they both outperform the GRAPE model.