Lithological facies classification is a pivotal task in petroleum geology, underpinning reservoir characterization and influencing decision-making in exploration and production operations. Traditional classification methods, such as support vector machines and Gaussian process classifiers, often struggle with the complexity and nonlinearity of geological data, leading to suboptimal performance. Moreover, numerous prevalent approaches fail to adequately consider the inherent dependencies in the sequence of measurements from adjacent depths in a well. A novel approach leveraging an attention-based gated recurrent unit (AGRU) model is introduced in this paper to address these challenges. The AGRU model excels by exploiting the sequential nature of well-log data and capturing long-range dependencies through an attention mechanism. This model enables a flexible and context-dependent weighting of different parts of the sequence, enhancing the discernment of key features for classification. The proposed method was validated on two publicly available datasets. Results demonstrate a considerably improvement over traditional methods. Specifically, the AGRU model achieved superior performance metrics considering precision, recall, and F1-score.