Graphene functionalized nanotips are expected to possess promising potential for various applications based on the outstanding electrical and mechanical properties of graphene. However, current methods, usually requiring a high growth temperature and identical crystal surface to match graphene lattice, are suitable for graphene formation on a flat surface. It remains a big challenge to grow graphene on a nanosized convex surface and fabricate functionalized nanotips with high quality graphene at the apex. In this work, a novel ultrafast annealing method is developed for growing large area graphene on Ni nanotips within 1-2 s. Few layered or multiple layered graphene is presented on the apex or sidewall of the conical tip surface. Direct experimental evidences support that thus-produced graphene is formed via the direct conversion of nickel carbide at the outer surface under the instantaneous high temperature, which is different from the conventional segregation mechanism. This newly developed ultrafast method provides a new route to produce graphene efficiently and economically, promising for both convex surfaces and flat substrates. Moreover, the graphene functionalized nanotips exhibit a great potential for nanoelectrical measurements and conductive scanning probe microscopy (SPM) applications.