The robotic intervention has great potential in the rehabilitation of post-stroke patients to regain their lost mobility. In this paper, firstly, we present a design of a novel, 7 degree-of-freedom (DOF) upper limb robotic exoskeleton (u-Rob) that features shoulder scapulohumeral rhythm with a wide range of motions (ROM) compared to other existing exoskeletons. An ergonomic shoulder mechanism with two passive DOF was included in the proposed exoskeleton to provide scapulohumeral motion with corresponding full ROM. Also, the joints of u-Rob have more range of motions compared to its existing counterparts. Secondly, we propose a fractional sliding mode control (FSMC) to control u-Rob. Applying the Lyapunov theory to the proposed control algorithm, we showed the stability of it. To control u-Rob, FSMC has shown effectiveness to handle unmodeled dynamics (e.g. friction, disturbance, etc.) in terms of better tracking and chatter compared to traditional SMC.