The 6- DOF joint robot with offset wrist can’t satisfy the Pieper rule,thus there are no closed- form inverse kinematics solutions for them. Compared with non- offset robot,a numerical iterative algorithm that integrates the closed- form inverse solutions of non- offset robot with the modified Newton iteration method is obtained,and the inverse method is utilized to obtain the closed- form inverse solutions of the non- offset robot with the same configurations,and the solutions are considered as the initial values of the subsequent iteration. According to the forward kinematics,by combining the three components of position vector with the three independent elements of attitude matrix,a non- liner equation set which contains all joint variables can be obtained,and then the numerical inverse kinematics solutions for the robot with offset wrist can be searched with the modified Newton iteration method. A large number of tests indicate that the algorithm can meet the requirements of real- time control.