We investigated the ferroelectric domain-wall propagation in epitaxial Pb(Zr,Ti)O3 thin film over a wide temperature range (3-300 K). We measured the domain-wall velocity under various electric fields and found that the velocity data is strongly nonlinear with electric fields, especially at low temperature. We found that, as one of surface growth issues, our domain-wall velocity data from ferroelectric epitaxial film could be classified into the creep, depinning, and flow regimes due to competition between disorder and elasticity. The measured values of velocity and dynamical exponents indicate that the ferroelectric domain walls in the epitaxial films are fractal and pinned by a disorder-induced local field.