Automatic Modulation Classification (AMC) represents a technique utilised to discern the modulation scheme employed in radio signals at the receiver's end. This holds substantial importance within intelligent receivers, which serve as pivotal components for upcoming wireless communication technologies like cognitive radio and adaptive modulation. Deep learning (DL) has gained widespread use in automatic modulation classification due to its exceptional learning capabilities and enhanced performance. In this paper, we introduce a novel hybrid dual-stream structure that combines a Convolutional Neural Network (CNN) and Gated Recurrent Unit (GRU) architecture for the classification of seven distinct digital modulation types (QAM16, CPFSK, 8PSK, QAM64, GFSK, BPSK, QPSK). Furthermore, we incorporate an attention mechanism to augment the performance of model. Notably, the utilization of two streams yields more effective outcomes compared to employing single-stream configurations. When compared with state-of-the-art approaches, our proposed model exhibits superior classification accuracy while concurrently reducing complexity. This streamlined architecture significantly enhances both training and classification efficiency.