The identification of lithology while drilling with horizontal well bit is a difficult problem to solve in geosteering. However, due to the existence of “zero length” (the distance between the logging tool and the bit), the lithology at the horizontal well bit cannot be accurately interpreted in real time, which creates a lag in geosteering. Based on logging while drilling (LWD) technology, this paper uses supervised learning in machine learning methods, conventional logging interpretation technology and big data idea in modern computer science, through interdisciplinary theories and methods to research lithology prediction for horizontal well bits in reservoirs. First, a measurement point and vertical reservoir boundary distance (D-MP-VRB) database is built according to different step size categories. Second, based on the D-MP-VRB database, D-MP-VRB prediction models are established using one-versus-one support vector machines (OVO SVMs), random forest (RF), neural networks (NN), and extreme gradient boosting tree (XGBoost) algorithms. To reduce the dimensions of the input data, the feature parameters of the samples are obtained by a correlation analysis of the logging data. The optimal parameter values of each algorithm are determined by grid search and 10-fold cross-validation methods. Finally, the prediction formula of the bit and vertical reservoir boundary distance based on the D-MP-VRB prediction model is established. A case study is performed with data from a sandstone reservoir in Changqing oilfield, Ordos Basin, China. On this basis, the lithology predictions at the bit in real time are carried out by using four models. Considering the principle of model prediction accuracy, through 1320 experiments, only the XGBoost prediction model can be selected, and the step size of the target category is 2 m, however, this model takes the longest time to train. Therefore, the reliable prediction model trained by the sample data of the original training set is used to predict the reservoir information encountered by horizontal well. After the newly drilled reservoir information has accumulated to a certain amount and accurately explained, it is added to the original training set sample data, and the prediction model is retrained to improve the accuracy and adaptability of the model. Based on the prediction results of the XGBoost model and the prediction formula, the distance prediction between the horizontal well bit and the vertical reservoir boundary is realized, real-time lithology correction at the bit is realized, and the adverse effect of the “zero length” on the lithology prediction at the bit is reduced. The research results provide not only a new method for the real-time prediction of lithology in horizontal well bits but also a theoretical basis for the geosteering of oilfield development and valuable information for future research.