With the high proportion of new energy with different control characteristics connected to the power grid, the problem of voltage support capability evaluation of power system has been paid more and more attention by scholars. Currently, inverters of renewable energy sources (RESs) are used to regulate bus voltages in distribution networks. Hence, it is important to evaluate the voltage support capacity of RESs. In this paper, the system voltage sensitivity matrix is first obtained by using the Jacobian matrix. An effective index based on the voltage sensitivity matrix to denote the voltage support capacity of the RESs is proposed. Then, a novel Lagrange extremum based optimization method is devised to obtain the maximum index and the optimal power injection. A standard IEEE123 bus system is applied for validation of the proposed method. In the simulation, five different operating conditions in the power limit range are considered, including the extreme point calculated by Lagrange's extreme value method, the boundary point on both sides of the extreme point and the point inside the boundary point. The simulation results validate that the Lagrange extremum method can efficiently evaluate the voltage support capacity, and maximize the voltage profile improvement.