The ability to describe local geometric shapes is very important for the representation of irregular point cloud. However, the existing network is still difficult to effectively capture accurate local shape information. This study simulates depthwise separable convolution calculation method in the point cloud and proposes a new type of convolution, namely dynamic cover convolution (DC-Conv), to aggregate local features. The core of DC-Conv is the space cover operator (SCOP), which constructs anisotropic spatial geometry in a local area to cover the local feature space to enhance the compactness of local features. DC-Conv achieves the capture of local shapes by dynamically combining multiple SCOPs in the local neighborhood. Among them, the attention coefficients of the SCOPs are adaptively learned from the point position in a data-driven way. Experiments on the 3D point cloud shape recognition benchmark dataset ModelNet40, ModelNet10, and ScanObjectNN show that this method can effectively improve the performance of 3D point cloud shape recognition and robustness to sparse point clouds even in the case of a single scale. Finally, sufficient ablation experiments are also provided to verify the effectiveness of the method. The open-source code is published at https://github.com/changshuowang/DC-CNN.