Aiming at the inverse dynamic solver of a multi-degree-of-freedom (DOF) industrial manipulator, a inverse dynamic recursive algorithm based on decoupled natural orthogonal complement was proposed. The velocity constraint was described by 6-dimensional twist vector, and the relation between joint velocities and twist vector was constructed by using the natural orthogonal complement matrix. The dynamical model of the manipulator was modelled by using the non-decoupled Newton-Euler equation. Considering the velocity constraint, the dynamical model was decoupled by using the natural orthogonal complement method to form the inverse dynamic recursive algorithm for the manipulator, and the least order form of the dynamics model was obtained. Taking a KUKA KR5 6-DOF manipulator as an example, the effectiveness of the proposed algorithm was verified in simulation environment.The results show that compared with other four algorithms, the proposed algorithm has lower computational complexity and higher computational efficiency; the calculation efficiency of this algorithm is 67.7% higher than that of ADAMS.