The dynamic properties of proton conductivity along hydrogen-bonded molecular systems,for example,ice crystal,with structure disorder or damping and finite temperatures exposed in an externally applied electric-field have been numerically studied by Runge-Kutta way in our Soliton model.The results obtained show that the proton-soliton is very robust against the structure disorder including the fluctuation of the force constant and disorder in the sequence of masses and thermal perturbation and damping of medium,the velocity of its conductivity increases with increasing of the externally applied electric-field and decreasing of the damping coefficient of medium,but the proton-soliton disperses for quite great fluctuation of the force constant and damping coefficient.In the numerical simulation we find that the proton-soliton in our model is thermally stable in a large region of temperature of T ≤ 273 K under influences of damping and externally applied electric-field in ice crystal.This shows that our model is available and appropriate to ice.