Magnetic field energy harvester (MEH) based on current transformers has emerged as a promising method for powering mass sensors in smart grids. However, a significant challenge lies in the insufficient power harvested at low primary currents. Aiming at resolving this shortcoming, a novel maximum power point (MPP) reaching method based on a low-power analog control circuit is proposed in the present study. The main objective of this method is to improve the performance of the MEH. The MPP is achieved by controlling the voltage of the dc side of the rectifier bridge based on the optimal load voltage characteristics of the MEH. The analog control circuit is designed using low-power analog devices and megaohm-level resistors, eliminating the need for a microcontroller. The performed analyses revealed that the calculated maximum power loss of the proposed approach is only 81.81 μW. Experimental results demonstrate a remarkable increase in MEH power output ranging from 101.39% to 149.89% compared to commercial circuits at currents ranging from 1 to 10 A.