This paper presents an efficient method for adaptive control of humanoid robot arms with biarticular muscles, which exhibits multiple beneficial properties. In our approach, sliding control was chosen to get joint torque first and then the joint torque was distributed to muscle forces. The muscle force was computed based on a Jacobian matrix between joint torque space and muscle force space. In addition, internal forces were used to optimize the computed muscle forces - and thus, two important benefits arise: through our proposed method, not only we are making sure that each muscle force stays within its predefined force boundary; but we are also enabling the muscles to work in the middle of their working range, which is considered to be an anti-fatigue state. Yet more benefit derived, comes from the fact that in our method all the dynamic parameters are updated in real-time, and can thus one can account for perturbations and disturbances during operation. Compared with previous work in parameter adaptation, a composite method was proposed which utilizes the prediction error to accelerate parameter convergence speed. Our method was tested for the case of reaching motions. The results clearly illustrate the benefits of the method.