The accurate classification of rocks is crucial for applications such as earthquake prediction, resource exploration, and geological analysis. Traditional methods rely on expert examination of thin-section images under a microscope, making the process time-consuming and prone to errors. Recent advancements in deep learning have emerged as a powerful tool for automated rock classification; however, distinguishing between similar rock types such as sedimentary, metamorphic, and magmatic rocks remains a challenge. This study proposes a novel hybrid convolutional neural network (CNN) approach that combines the strengths of VGG16 and EfficientNetV2 architectures for the classification of thin-section rock images. The model, developed using the Feature-Selected Hybrid Network (FSHNet), demonstrates significant improvements over individual models, achieving a 5% increase in accuracy compared to Efficient-NetV2B0 and a 9% increase compared to VGG16. By employing the ReliefF algorithm for feature selection and Support Vector Machines (SVMs) for classification, the model further reduces the dimensionality of the feature space, enhancing computational efficiency. The proposed model has been applied to two different rock datasets. The first dataset consists of 2634 images, categorized into sedimentary, metamorphic, and magmatic rock classes. Additionally, the approach was tested on a second dataset comprising petrographic microfacies images, demonstrating its effectiveness in multiclass geological structure classification. Validation on both datasets shows that the proposed method outperforms popular deep learning models and previous studies, achieving a 3% increase in accuracy. These results highlight that the proposed approach provides a robust and efficient solution for automated rock classification, offering significant advancements for geological research and real-world applications.