  The phase transition of a Bardeen black hole is studied by considering
Ehrenfest's equations. The thermodynamic variables such as entropy, potential
and heat capacity are calculated from the first law of thermodynamics for black
holes. That no discontinuity in entropy and potential of the black holes means
that the first order phase transition will not generate for the Bardeen black
holes. However, the divergence of heat capacity at constant potential and
satisfaction of the Ehrenfest's equations indicates that the second order phase
transition of Bardeen black hole will appear.
