The 3-translational parallel mechanism is widely used in industrial, medical, and military fields, among others. With the development of the national logistics industry, a pressing need for a kind of 3-translational parallel mechanism emerged. Such mechanisms have high stiffness and high bearing capacity and are used for cargo handling and sorting. A novel method based on the graphical approach was proposed for the synthesis of 3-translational redundancy actuated parallel mechanism with closed-loop branch chains. The new mechanism has four symmetrically arranged branch chains, which eases subsequent kinematics and dynamics analyses while providing good mechanical properties. Based on the graphical approach theory, according to the constraint number contained in the branch chain, two types of redundant driven branch chains with closed-loop structures were constructed. The first type includes rotation constraint in one direction, while the second type includes the rotation constraint in two directions. Based on various combinations of two branch chain types, their allocation schemes can be divided into two types. Moreover, said these two allocation schemes can be integrated into at least 500 and 400 types of 3-translational redundant actuated parallel mechanisms with closed-loop branch chains. Then, the degree of freedom properties of representative mechanisms were tested using the screw theory. A large number of novel mechanisms were integrated assessed using this method, and branch chains such mechanisms were symmetrically distributed. They have a strong bearing capacity, simple calculation, and control, and can be applied to the handling and sorting of goods, large-scale precision machine tools, and large construction machinery vibration isolation systems, among others.