This paper describes an algorithm for minimal turning complete coverage Path planning for cleaning robots. This algorithm divides the whole cleaning area by cellular decomposition, and then provides the path planning among the cells employing a flow network. It also provides specific path planning inside each cell guaranteeing the minimal turning of the robots. The minimal turning of the robots is directly related to the faster motion and energy saving. The proposed algorithm is compared with previous approaches in simulation and the result shows the validity of the algorithm.