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To mitigate the impact of low-frequency noise from the tunnel magnetoresistance (TMR) current sensor and ambient stray magnetic fields on weak current detection accuracy, we propose a high-resolution modulation-demodulation test method. This method modulates and demodulates the measurement signal, shifting low-frequency noise to the high-frequency band for effective filtering, thereby isolating the target signal from the noise. In this study, we developed a Simulink model for the TMR current sensor modulation-demodulation test method. Practical time-domain and frequency-domain tests of the developed high-resolution modulation-demodulation method revealed that the TMR current sensor exhibits a nonlinearity as low as 0.045%, an enhanced signal-to-noise ratio (SNR) of 77 dB, and a heightened resolution of 100 nA. The findings indicate that this modulation-demodulation test method effectively reduces the impact of low-frequency noise on TMR current sensors and can be extended to other types of resistive devices.