According to the closed solution and numerical solution for the inverse kinematics of the robot, taking the 5 degree of freedom series robot HC5R as an example, the traditional closed solution of HC5R was briefly introduced.Then, a method of Jacobian matrix iterative based on forward kinematics was elaborated.The 2 methods were used to solve the inverse kinematics of T1、T2、T3 in HC5R robot’s reachable space. The conclusion is: numerical solution method is more general relatively to closed solution, but the iteration process is complex,and more computational resource is required,so it takes a long time,also the result of the solution is only one;by comparison, closed solution is usually used in practical engineering,by which all the results can be solved more quickly.