Traditional aerodynamic shape optimization (ASO) is costly and time-intensive, requiring extensive manual tuning for parameterization to define the design space and manipulate geometries. Conventional parameterization methods limit flexibility and demand specialized knowledge, making efficient ASO challenging. We introduce the deep geometric mapping (DeepGeo) model, a neural-network-based approach that automates parameterization, accelerating ASO and reducing costs. By leveraging the expressive capacity of neural networks, DeepGeo handles large shape deformation while preserving global surface smoothness, allowing efficient optimization in high-dimensional design spaces. Eliminating the need for training datasets and manual hyperparameter tuning and integrating computational fluid dynamics (CFD) mesh deformation, DeepGeo significantly lowers ASO’s implementation complexity and cost. Case studies, including two-dimensional circle, Common Research Model wing, and blended-wing–body aircraft optimization, validate DeepGeo’s effectiveness, achieving results comparable to state-of-the-art free-form deformation with minimal manual intervention. This work positions DeepGeo as a novel and effective parameterization framework that streamlines the workflow and reduces implementation complexity in advanced ASO.