In order to solve the problem of space manipulator path planning with minimum energy consumption, the energy function of space manipulator is derived first, and then the energy function is regarded as the functional of 3 joint angle functions. The problem of space manipulator path planning with minimum energy consumption is translated into a problem of the functional extreme with fixed boundary. A system of equations for expressing the path with minimum energy consumption is derived from resolving the problem of the functional extreme by using variational method. By means of the inverse matrix expression of the upper triangular matrix, the system of 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. For a group of parameters of the 3R manipulator, the initial value problem of the new system of equations is solved by using Matlab simulation method. The solution of the boundary value problem of the new system of equations, representing the path with minimum energy consumption, is obtained from the solutions of initial value problem of the same system of equations by using random search method, and the feasibility of variational method for solving this kind of problem is also validated.