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In order to meet the requirement of multi-angle operation in industrial pick-and-place applications, a novel six degree-of-freedom (DOF) Delta robot with three sets of symmetrically distributed coupled branches was proposed. Firstly, the 6-DOF Delta robot was decomposed into three sets of coupled branches, which can be regarded as independent motion units and can be further treated as equivalent serial chains. The mobility of the overall parallel mechanism was analyzed based on the screw theory to demonstrate that it had three rotational and three translational motion capabilities. Secondly, since each set of coupled branches contained two kinematic chain, the closedloop vector method was used to calculate the inverse position solution of two chain in the coupled branch, based on which an inverse kinematic model of the proposed robot was established. Furthermore, a search algorithm was proposed to describe the robot’s workspace under the boundary condition which was compared with that of a traditional 3-DOF Delta robot at the same parameter level. Simulation results showed that the workspace of a traditional 3-DOF Delta robot was a subset of that of the proposed 6-DOF Delta robot. Finally, the kinematic experiments were carried out on the engineering prototype, the results showed that the proposed robot had three degree-of-reedom of rotation and three degree-of-freedom translational motion, and can achieve multi-angle grabbing operation. In the robot workspace, the limit position of the typical motion plane was consistent with the simulation analysis results.