Due to the numerous challenges associated with CFD calculations and high-dimensional data processing, it is challenging for the current approaches to satisfy the demands of inverse design of three-dimensional aerodynamic configuration. This work provides an effective inverse design method for three-dimensional aerodynamic configuration based on Isometric Feature Mapping (ISOMAP) in manifold learning. In this approach, the aerodynamic shape and parameterized control volume are regarded as the spatial nonlinear coupling surface, which is then projected into the low-dimensional manifold space via the ISOMAP approach to producing the manifold structure. The deformation control points' pressure distribution, which is paired with the samples to create a snapshot matrix, is interpolated from the resultant manifold structure. The Gappy POD (Proper Orthogonal Decomposition) approach is then employed to complete the missing design variables within the target pressure distribution of the deformation control points. The original aerodynamic shape is then parameterized using the FFD (Free Form Deform) method to create an aerodynamic shape that matches the target pressure distribution. The M6 wing and the RAE2822 wing are used as the initial models to verify the design method. The aerodynamic response error of the inverse design wing and the target wing is within 2%. The results demonstrate that the proposed three-dimensional aerodynamic shape inverse design approach has a high design accuracy, dramatically improves design efficiency, and significantly reduces the dimensionality required for three-dimensional aerodynamic shape inverse design.