This paper deals with the problem of safe grasping of an object. According to robot maneuvers during of movement, the slipping or falling of the objects is possible. Here, an adaptive backstepping control method is used for controlling of slipping and tracking of desirable paths. First, the robot dynamics of grasping of an object including mechanical arm with three rotational joints, one prismatic joint, jaw gripper as well as dynamic of the electrical actuators is derived. Then, backstepping technique, which is a systematic approach based on Lyaponov theory, is applied for this nonlinear system. Beacuse of existence of different uncertainties in this system such as mass and inertia of robot and object mass, it is required to design a controller to be able to cope with these uncertainties. Accordingly, a stable controller using adaptive backstepping control methodology is also designed to estimate of these parameters’ uncertainties. Stability analysis is provided based on Lyapunov theory. Simulations are carried out to evaluate the performance of the proposed controller. Results show the effectiveness of the proposed control method.