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Currently, many different network architectures have been explored in speaker verification, including time-delay neural network (TDNN), convolutional neural network (CNN), transformer and multi-layer perceptrons (MLP). However, hybrid networks with diverse structures are rarely investigated. In this paper, we present a novel and effective dual path embedding learning framework, named Dual Path Network (DPNet), for speaker verification with triplet attention. A new topology of integrating CNN with a separate recurrent layer connection path internally is designed, which introduces the sequential structure along depth into CNN. This new architecture inherits both advantages of residual and recurrent networks, enabling better feature re-usage and re-exploitation. Additionally, an efficient triplet attention module is utilized to capture cross-dimension interactions between features. The experimental results conducted on Voxceleb dataset show that our proposed hybrid network with triplet attention can outperform the corresponding ResNet by a significant margin.