The dynamic phase transition of charged dilaton black holes is investigated in this paper.The Gibbs free energy landscape is introduced,and the corresponding GL is calculated for the dilaton black hole.We numerically solve the Fokker-Planck equation constrained by only the reflecting boundary condition.The effects of dilaton grav-ity on the probabilistic evolution of dilaton black holes are explored.Firstly,the horizon radius difference between a large dilaton black hole and a small dilaton black hole increases with the parameter α.Secondly,with increasing α,the system needs much more time to achieve a stationary distribution.Finally,the values attained for ρ(rl,t)and ρ(rs,t)vary with α.Additionally,by resolving the Fokker-Planck equation constrained by both the reflecting bound-ary condition and absorbing boundary condition,we investigate the first passage process of dilaton black holes.The initial peak decays more slowly with increasingα,which can also be observed via the slowing decay of Σ(t)(the sum of the probability of the black hole system not having completed a first passage by time t).Moreover,the time cor-responding to the single peak of the first passage time distribution is found to increase with the parameter α.Consid-ering these observations,the dilaton field is found to slow down the dynamic phase transition process between a large black hole and a small black hole.