This paper reports a high-resolution, template-free, and direct-printing method of functional nanofiber on 3D surfaces using a self-aligning nanojet (SA-N) in near-field electrospinning (NFES). In the lowest regime of NFES, the cone-jet transition is induced by the surface current, which leads to a unique jetting configuration where the microscale Taylor cone (microcone) is formed on the surface of the spherical-shape droplet. The microcone rapidly develops to the nanoscale jet where the tangential electric force dominates the kinematics of the charged jet. The spherical-shape ejection boundary allows the jetting angle from 0 degrees to +/- 90 degrees in both convex and concave surfaces, enabling precise deposition of nanofiber regardless of the curvature of the 3D surfaces. Using SA-N, precise printing of functional nanofiber is successfully demonstrated on various 3D geometries, including convex, concave, and inner surface of the 3D structure. The direct-printing ability of nanofiber on 3D surfaces using SA-N will be a promising strategy to utilize various functional polymers in flexible electronics, printed electronics, optics, and biomedical engineering.