Tunnel magnetoresistance (TMR) can measure weak magnetic fields and has significant advantages for use in alternating current/direct current (AC/DC) leakage current sensors for power equipment; however, TMR current sensors are easily perturbed by external magnetic fields, and their measurement accuracy and measurement stability are limited in complex engineering application environments. To enhance the TMR sensor measurement performance, this paper proposes a new multi-stage TMR weak AC/DC sensor structure with high measurement sensitivity and anti-magnetic interference capability. The front-end magnetic measurement characteristics and interference immunity of the multi-stage TMR sensor are found to be closely related to the multi-stage ring size design via finite element simulation. The optimal size of the multipole magnetic ring is determined using an improved non-dominated ranking genetic algorithm (ACGWO-BP-NSGA-II) to derive the optimal sensor structure. Experimental results demonstrate that the newly designed multi-stage TMR current sensor has a measurement range of 60 mA, a fitting nonlinearity error of less than 1%, a measurement bandwidth of 0–80 kHz, a minimum AC measurement value of 85 μA and a minimum DC measurement value of 50 μA, as well as a strong external electromagnetic interference. The TMR sensor can effectively enhance measurement precision and stability in the presence of intense external electromagnetic interference.