The asymmetrical shape of the off-axis aspheric surface and the nonlinear change of its surface curvature bring challenges to the high-precision measurement of surface shape. In order to solve the problem that existing off-axis aspheric surface shape measurement methods were highly dependent on precise initial alignment of the test piece and showed poor adaptability to curvature variations， we proposed a spatially-constrained differential confocal adaptive measurement method to achieve adaptive and high-precision measurement of off-axis aspheric surfaces without initial pose dependence. First， based on the translation-rotation scanning measurement principle and the demonstrated performance of differential confocal technology in anti-surface inclination accurate fixed focusing， we developed a spatial constraint model incorporating both distance and tilt angle parameters between designed measurement points and actual test locations. This model enabled optimized spiral scanning path planning with curvature-adaptive adjustment capability for off-axis aspheric surfaces. Experimental verification demonstrated surface form accuracy with root mean square （RMS） errors below 10 nanometers and 3σ values under 5 nanometers compared to Zygo interferometer references， meeting the requirements of high-precision measurement of off-axis aspheric surfaces.