In this paper, we propose a new on-line coverage algorithm, which we call deadline coverage. The algorithm has an assumption that robot does not know the map of environments for coverage in advance. To cope with the unknown environment, deadline coverage algorithm integrates with a SLAM solution. Because the robot does not know the map for coverage in advance, not like the previous coverage, the goal of deadline coverage algorithm is not to minimize the complete coverage time but to maximize the coverage efficiency in real time. Experimental results show that the deadline coverage algorithm outperforms previous algorithms for unknown environments.