Geometric discontinuities in the deformation transition section of trailing-edge variable-camber wings and inconsistencies between optimization design and experimental verification are commonly induced. Taking the NACA63a612 laminar airfoil as the research object, a parameterization method integrating least-squares polynomial characterization and non-uniform B-spline transition correction is proposed to ensure full continuous and smooth airfoil deformation. Three-dimensional compressible RANS equations and the Spalart–Allmaras turbulence model are adopted for numerical simulation, and the proposed method is verified via wind tunnel tests. The influences of trailing-edge deflection angle are investigated under low and high-speed conditions. Low-speed lift and lift-to-drag ratio are effectively enhanced by downward deflection; high-speed large downward deflection reduces critical Mach number and critical angle of attack, while small deflections deliver superior aerodynamic performance. A multi-island genetic algorithm is implemented for multi-objective optimization with lift coefficient and lift-to-drag ratio as optimization objectives, and airfoil continuity, deformation boundary and thickness distribution as constraint conditions. Compared with the baseline airfoil, the optimized design achieves low-speed lift coefficient and lift-to-drag ratio increments of 52.8% and 18.2%, as well as high-speed increments of 48.6% and 9.8%. Variable-camber wing models are manufactured by 3D printing and tested in low-speed wind tunnels, establishing a complete research framework of geometric modeling, aerodynamic optimization and experimental verification. CFD and optimization results are well consistent with experimental data. This study provides a reference for the aerodynamic design and optimization of trailing-edge variable-camber airfoils.