Smishing attacks, a sophisticated form of cybersecurity threats conducted via Short Message Service (SMS), have escalated in complexity with the widespread adoption of mobile devices, making it increasingly challenging for individuals to distinguish between legitimate and malicious messages. Traditional phishing detection methods, such as feature-based, rule-based, heuristic, and blacklist approaches, have struggled to keep pace with the rapidly evolving tactics employed by attackers. To enhance cybersecurity and address these challenges, this paper proposes a hybrid deep learning approach that combines Bidirectional Gated Recurrent Units (Bi-GRUs) and Convolutional Neural Networks (CNNs), referred to as CNN-Bi-GRU, for the accurate identification and classification of smishing attacks. The SMS Phishing Collection dataset was used, with a preparatory procedure involving the transformation of unstructured text data into numerical representations and the training of Word2Vec on preprocessed text. Experimental results demonstrate that the proposed CNN-Bi-GRU model outperforms existing approaches, achieving an overall highest accuracy of 99.82% in detecting SMS phishing messages. This study provides an empirical analysis of the effectiveness of hybrid deep learning techniques for SMS phishing detection, offering a more precise and efficient solution to enhance cybersecurity in mobile communications.