This paper describes Cartesian position and force control with adaptive impedance/compliance capabilities for a humanoid robot arm including velocity control incorporate with End-Effector Fixation Control (EEFC). We successfully demonstrated the end-effector positioning to reach the target point in Cartesian coordinate frame based on force control without solving the inverse kinematic problem. The advantage of this function is obvious in moving the end-effector to go to the target point safely because the robot arm can be stopped or disturbed during the movement. The impedance gain can be adjusted adaptively according to the moving trajectory conditions. As the result, the end-effector can reach the presetting target point. We also have experimentally demonstrated the effect of adaptive impedance/compliance control, velocity control and EEFC which are useful in many applications, such as laparoscopic surgery, industrial taper cutting compensation and feeding food to the impaired person.