Friction mine installation uses friction between steel wire rope and sheave wheel to convey load. Wire rope silppage often occurs during emergency braking phase, which has negative impact on the safe operation of the hoist. In this paper, the slip characteristics of steel wire rope under constant-deceleration-emergency-braking (CDEB) for short condition are investigated. A limit deceleration calculation method is proposed, in which an acceleration deviation is defined to normalize the longitudinal acceleration of the cage under CDEB condition, and the sudden increase of the acceleration deviation coefficent is used to determine whether the slip happens, as to obtain the limit deceleration. A series of limit deceleration values under CDEB condition are obtained by the combination of an experimentally validated simulation model and the proposed method in this paper. Then, the following limit deceleration prediction models are achieved by means of linear fitting, ax = -k1M + b1 (lowing stage) and ax = k2M + b2 (lifting stage). These prediction models will contribute to the determination of the range of constant deceleration braking point, thereby laying a foundation for the development of anti-skid strategy for friction mine installation.