Cervical cancer screening relies on accurate cell classification. Approaches based on Convolutional Neural Networks (CNNs) have proven effective in addressing the task. However, these approaches suffer from two main challenges. First, they may introduce bias into models due to variations in cell morphology and color. Second, they may struggle to capture broader contextual information as CNNs primarily focus on local pixel information. To address these issues, we present a novel hybrid model named DualBranch-FusionNet, which combines CNNs for local feature extraction with Transformers for capturing global contextual information to improve cervical cell classification accuracy. The proposed method adopts the three-fold ideas. First, concerning the CNN branch, it introduces Omni-dimensional Dynamic Convolution (ODConv) to adaptively extract detailed features across multiple dimensions and designs an Adaptive Channel Modulation (ACM) mechanism to dynamically emphasize critical feature channels. Second, regarding the Transformer branch, it designs a Dynamic Query-Aware Sparse Attention (DQSA) mechanism to effectively filter out less relevant key-value pairs over a larger receptive field, thereby reducing the interference of irrelevant information. Third, it adopts a fusion strategy, the Simple Fusion Module (SFM), to produce more comprehensive feature representations, leading to improved cervical cell classification accuracy. The proposed model was validated on two datasets: the Mendeley LBC and the Tianchi Cervical Cancer Risk Intelligent Diagnosis Challenge datasets, achieving Accuracies of 99.07% and 99.12%, respectively.