Melting of sea ice in Arctic areas has opened up new horizons for the development of Arctic Marine Transportation Systems (AMTS). An icebreaker assists a single ship if the ice classification of the ship does not meet the ice conditions. With the increase of the number of ships and escort operations, the risks of collisions between escorting ships (icebreakers) and escorted ships have also increased. In view of this, a calculation model of the safety distance and collision risks between escorting and escorted ships is proposed in this paper in order to facilitate safe navigation in Arctic ice-covered waters. The aim of the paper is to analyze features of navigation concerning icebreakers and escorted ships in escort operations under continuous icebreaking conditions, where a quantitative model is proposed to calculate safety distances under varying ice conditions based on the ship-following theory. The proposed model is able to quantify safety distance intervals at an acceptable collision frequency under varying ice conditions, as well as the movement characteristics of icebreakers and escorted ships. A case study is carried out to calculate the safety distance between “YONG SHENG” and “50 LET POBEDY”. The results show that the model can accurately calculate the safety distance between “YONG SHENG” and “50 LET POBEDY”, which can provide theoretical guidance for ice navigation.