Eight-degree-of-freedom redundant manipulators are considered more suitable for performing special tasks in unstructured environments due to their high degree of freedom and flexibility. The 8-DOF tunnel shotcrete manipulator is a kind of equipment that is applied to the concrete spraying support in the process of tunnel excavation. Since the mechanism itself is a redundant manipulator with link offset, its inverse kinematics is extremely difficult to solve. To address the problems that the conventional redundant manipulator inverse kinematics solution is difficult to solve analytically and the numerical algorithm requires several iterations with accumulated errors, a synthesis inverse kinematics algorithm based on the weighted minimum norm method and the joint angle parameterization method is proposed to overcome these defects. Firstly, a set of optimized joint angle approximation solutions is obtained based on the weighted least norm method of joint angle limit avoidance optimization function, and secondly, two joint variables are parameterized as known parameters in the optimized approximation solutions based on the joint angle parameterization method, and further, the analytical expressions of the remaining joint angles are derived by algebraic methods. Finally, the superiority of the inverse kinematic synthesis algorithm over the joint angle parameterization method in terms of joint motion is verified by comparing numerical examples of linear motion trajectories. Numerical simulation results show that the algorithm has the advantages of avoiding joint angle limits, high computational accuracy, no cumulative error, and the algorithm can meet the general real-time motion control requirements as demonstrated by the experimental analysis of algorithm time consumption.