In order to search out the shortest path of the 3R manipulator, a path length expression of manipulator’s end-effectors is given first, and then the problem is modeled as a functional extreme problem. For the purpose of simplifying the solving process, the functional extreme problem is translated into a new one with the same solution, and the solution of the latter expressed by a system of differential equations is derived by using variational method. By means of the inverse matrix expression of the upper triangular matrix, the system of differential equations is translated into a new one consisted of normal state equations. The method can avoid complex inverse matrix computing, and make the computation of the transition process simpler when compared with differential geometry method. By using Matlab simulation method, 3 joint angle functions corresponding to the shortest path of the 3R manipulator’s end-effectors is obtained.