The defocus deblurring raised from the finite aperture size and exposure time is an essential problem in the computational photography. It is very challenging because the blur kernel is spatially varying and difficult to estimate by traditional methods. Due to its great breakthrough in low-level tasks, convolutional neural networks (CNNs) have been introduced to the defocus deblurring problem and achieved significant progress. However, they apply the same kernel for different regions of the defocus blurred images, thus it is difficult to handle these nonuniform blurred images. To this end, this study designs a novel blur-aware multi-branch network (BaMBNet), in which different regions (with different blur amounts) should be treated differentially. In particular, we estimate the blur amounts of different regions by the internal geometric constraint of the DP data, which measures the defocus disparity between the left and right views. Based on the assumption that different image regions with different blur amounts have different deblurring difficulties, we leverage different networks with different capacities (emph{i.e.} parameters) to process different image regions. Moreover, we introduce a meta-learning defocus mask generation algorithm to assign each pixel to a proper branch. In this way, we can expect to well maintain the information of the clear regions while recovering the missing details of the blurred regions. Both quantitative and qualitative experiments demonstrate that our BaMBNet outperforms the state-of-the-art methods. Source code will be available at https://github.com/junjun-jiang/BaMBNet.