An annealing apparatus includes: a temperature-gradient preheating unit, configured for performing a gradient-preheating process for a substrate that is to be annealed by using a gradient temperature; a high temperature heating unit, configured for performing a high temperature heating process for the preheated substrate; and a shifting device, configured for transporting the substrate from the temperature-gradient preheating unit to the high temperature heating unit when and/or after the substrate is subjected to the gradient-preheating process. The annealing apparatus adopts a gradient heating method to perform a preheating treatment for the substrate, so the annealing efficiency is increased. An annealing process that uses the annealing apparatus is further provided.