Rice is an essential staple food worldwide that is important in promoting international trade, economic growth, and nutrition. Asian countries such as China, India, Pakistan, Thailand, Vietnam, and Indonesia are notable for their significant contribution to the cultivation and utilization of rice. These nations are also known for cultivating different rice grains, including short and long grains. These sizes are further classified as basmati, jasmine, kainat saila, ipsala, arborio, etc., catering to diverse culinary preferences and cultural traditions. For both local and international trade, inspecting and maintaining the quality of rice grains to satisfy customers and preserve a country's reputation is necessary. Manual quality check and classification is quite a laborious and time-consuming process. It is also highly prone to mistakes. Therefore, an automatic solution must be proposed for the effective and efficient classification of different varieties of rice grains. This research paper presents an automatic framework based on a convolutional neural network (CNN) for classifying different varieties of rice grains. We evaluated the proposed model based on performance metrics such as accuracy, recall, precision, and F1-Score. The CNN model underwent rigorous training and validation, achieving a remarkable accuracy rate and a perfect area under each class's Receiver Operating Characteristic (ROC) curve. The confusion matrix analysis confirmed the model's effectiveness in distinguishing between the different rice varieties, indicating minimal misclassifications. Additionally, the integration of explainability techniques such as LIME (Local Interpretable Model-agnostic Explanations) and SHAP (SHapley Additive exPlanations) provided valuable insights into the model's decision-making process, revealing how specific features of the rice grains influenced classification outcomes.