One of the major bottlenecks of the traditional Current Transformer Energy Harvester (CTEH) is the instable output induced by the wide-range variations of the current in transmission lines. In this work, a novel CTEH capable of generating a stable output is demonstrated by using a core fabricated with saturable magnetic material. The stable output of the CTEH is enabled by the constant voltage-time product in its saturable characteristic. The proposed CTEH is implemented with a resistive load representing the load of electronic devices. When the current in the primary side of the CTEH’s increases from 1A to 1000A, the maximum power on the load can reach about 0.5W, demonstrating the feasibility of using the CTEH with the saturable magnetic core as a quasi-stable power supply.