A method of preparing a carbon fiber including: preparing a precursor fiber for preparing a carbon fiber; and stabilizing the precursor fiber. The stabilization of the precursor fiber includes a first stabilization phase, a second stabilization phase, a third stabilization phase, and a fourth stabilization phase, which are set at four different temperatures between a temperature at which heat starts to be generated from the stabilization reaction of the precursor fiber and a temperature at which the generation of heat is maximized. Ozone gas is input while at least one phase of the third stabilization phase and the fourth stabilization phase is carried out.