Hybrid models which combine the convolution and transformer model achieve impressive performance on human pose estimation. However, the existing hybrid models on human pose estimation, which typically stack self-attention modules after convolution, are prone to mutual conflict. The mutual conflict enforces one type of module to dominate over these hybrid sequential models. Consequently, the performance of higher-precision keypoints localization is not consistent with overall performance. To alleviate this mutual conflict, we developed a hybrid parallel network by parallelizing the self-attention modules and the convolution modules, which conduce to leverage the complementary capabilities effectively. The parallel network ensures that the self-attention branch tends to model the long-range dependency to enhance the semantic representation, whereas the local sensitivity of the convolution branch contributes to high-precision localization simultaneously. To further mitigate the conflict, we proposed a cross-branches attention module to gate the features generated by both branches along the channel dimension. The hybrid parallel network achieves75.6%and75.4%APon COCO validation and test-dev sets and achieves consistent performance on both higher-precision localization and overall performance. The experiments show that our hybrid parallel network is on par with the state-of-the-art human pose estimation models.