Shuttle based storage and retrieval systems (SBS/RS) attract continuous research attention because of their ability to achieve a high throughput. In an SBS/RS system, lifts are regarded as the bottleneck that hinder reaching higher throughput and therefore require subtle control polices. In this paper, the scheduling of two non-passing lifts on a common rail SBS/RS has been studied with consideration of the acceleration and deceleration of the lifts. Lift scheduling includes storage and retrieval requests sequencing, assignment of lifts, and collision avoidance. The main objective of the lift scheduling is minimizing the makespan of the moves. Different with the traditional constant velocity lift scheduling approach is that new collisions emerge when the acceleration/deceleration of the lifts are taken into consideration. This makes the scheduling different. In this paper a collision free lifts trajectory predicting approach with acceleration/deceleration is presented. Combined with the collision-free method, request sequencing and assignment are carried out by a proposed genetic algorithm. Experimental results with several SBS/RS practical working scenarios provide evidence that the proposed scheduling approach achieved on average 12.2% and 6.4% improvement in makespan compared with the constant velocity approach when the maximum velocity of the lifts is 1.5 m/s and 2 m/s respectively.