A sound field control method for synthesizing a desired amplitude distribution inside a target region, amplitude matching, is proposed. In the conventional pressure matching, a desired sound field is set as a pressure distribution including amplitude and phase. In personal audio applications, it is sometimes not necessary to synthesize a specific phase distribution, but a certain acoustic power level should be controlled inside the target region. Since the optimization problem to achieve amplitude matching becomes nonlinear, there is no closed-form solution and numerical optimization algorithms are generally applied. We derive an efficient algorithm for the amplitude matching based on the majorization-minimization algorithm. Numerical experiments indicated that high control accuracy over the target region can be achieved with low computational cost by using the proposed algorithm.