The authors present a globally convergent numerical method for coefficient inverse problems of elliptic partial differential equations. Generally, the solutions of inverse problems in gradient-based optimization methods are vitally influenced by the initial guesses, which is known as the issue of local minima. Due to this issue, the gradient-based optimization methods can limit their applications that admit variety of initial approximations. Hence, in this work, the authors give a method that converges to a good approximation being independent of the initial conditions (i.e., the authors refer to it as global convergence). The method is rigorously derived and numerically tested for a thermal tomography problem.