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.