The need for human body posture robots has led researchers to develop dexterous design of exoskeleton robots. Quantitative techniques to assess human motor function and generate commands for robots were required to be developed. In this paper, we present a passivity based adaptive control algorithm for upper limb assist exoskeleton. The proposed algorithm can adapt to different subject parameters and provide efficient response against the biomechanical variations caused by subject variations. Furthermore, we have employed the Particle Swarm Optimization technique to tune the controller gains. Efficacy of the proposed algorithm method is experimentally demonstrated using a seven degree of freedom upper limb assist exoskeleton robot. The proposed algorithm was found to estimate the desired motion and assist accordingly. This algorithm in conjunction with an upper limb assist exoskeleton robot may be very useful for elderly people to perform daily tasks.