The purpose of research on Multi-Robot Task Allocation （MRTA） is to improve the task completion efficiency of robots in smart factories. Aiming at the deficiency of the existing algorithms in dealing with large-scale multi-constrained MRTA， an MRTA Algorithm Combining Genetic Algorithm and Rolling Scheduling （ACGARS） was proposed. Firstly， the coding method based on Directed Acyclic Graph （DAG） was adopted in genetic algorithm to efficiently deal with the priority constraints among tasks. Then， the prior knowledge was added to the initial population of genetic algorithm to improve the search efficiency of the algorithm. Finally， a rolling scheduling strategy based on task groups was designed to reduce the scale of the problem to be solved， thereby solving large-scale problems efficiently. Experimental results on large-scale problem instances show that compared with the schemes generated by Constructive Heuristic Algorithm （CHA）， MinInterfere Algorithm （MIA）， and Genetic Algorithm with Penalty Strategy （GAPS）， the scheme generated by the proposed algorithm has the average order completion time shortened by 30.02%， 16.86% and 75.65% respectively when the number of task groups is 20， which verifies that the proposed algorithm can effectively shorten the average waiting time of orders and improve the efficiency of multi-robot task allocation.