Space exploration has become a major focus in the field of technology, with gear transmissions in aerospace equipment playing a crucial role. In the extreme environment of space, gear transmissions face challenges like large temperature differentials, deformation and maintenance difficulties, which will severely impact transmission accuracy and service life. To meet the growing demands for high-performance gear transmissions with high transmission efficiency and error adaptability in the aerospace field, this paper proposes a novel curve-surface conjugate internal gear drive consisting of an involute internal gear and a curve-surface gear. The fundamental theory of curve-surface conjugation is introduced, and the construction method for curve-surface gear based on a selected contact path and meshing tube is presented. The analysis models including induced curvature, sliding ratio and tooth contact analysis with errors (ETCA) are simulated to evaluate the meshing characteristics. Additionally, prototypes are manufactured and experimental setups are established to validate the transmission performance. These results indicate that as the rotational speed increases, the transmission efficiency of the curve-surface conjugate internal gear drive improves, which is contrary to the trend observed in involute gear drives. And the transmission efficiency of the curve-surface conjugate internal gear drive surpasses that of the involute gear drive at higher rotational speeds. Moreover, this novel gear drive exhibits excellent error adaptability, maintaining intact contact paths and high transmission efficiency even in the presence of assembly errors. This study provides new ideas for the design and manufacture of high-performance gear transmissions from the perspective of spatial geometric elements.