Seepage is a main cause of dam failure, and its stability analysis is the focus of a dam’s design, construction, and management. Because a geological survey can only determine the range of a dam foundation’s hydraulic conductivity, hydraulic conductivity inversion is crucial in engineering. However, current inversion methods of dam hydraulic conductivity are either not accurate enough or too complex to be directly used in engineering. Therefore, this paper proposes a new method for the inversion of hydraulic conductivity with high application value in hydraulic engineering using an improved genetic algorithm coupled with an unsaturated equivalent continuum model (IGA–UECM). This method is implemented by a new code that fully considers engineering applicability. In addition to overcoming the premature convergence shortcomings of traditional genetic algorithms, it converges faster than Bayesian optimization and tree-structured Parzen estimator inversion algorithms. This method is verified by comparing the water head from drilling exploration and inversion. The results of the inversion are used to study the influence of a cement grouting curtain layout scheme on the seepage field of the Hami concrete-face rockfill dam in China, which is used as an engineering application case of the IGA–UECM. The law of the seepage field is reasonable, which verifies the validity of the IGA–UECM. The new inversion method of hydraulic conductivity and the proposed cement grouting curtain layout in this study offer possible strategies for the design, construction, and management of concrete-face rockfill dams.