In this paper, we propose a method of trajectory planning for an object in pushing operation, which is to move the object on a floor to desired position and orientation using one arm. The feature of this method is that not only position and orientation of the object but also friction between the arm and the object are considered. We suppose that the distribution of magnitude of friction between the object and the floor is known. First, the state equation of the system and constraint equations about state and control variables are derived from kinematic constraints of the object. Then we make a performance index about distance, and translate the trajectory planning into an optimal control problem with state and input constraints. The trajectory of the object is obtained by solving the problem numerically. In the latter part of this paper, the trajectory planning is extended to that with obstacle avoidance. Numerical examples show the effectiveness of the proposed method.