The magnetic field sensor based on tunnel magnetoresistance (TMR) effect has potential applications in various fields due to its very high field sensitivity and low power comsuption. However, the resolution of magnetic sensor depends on not only field sensitivity, but also intrinsic noise level. The intrinsic noise of an electronic device is normally frequency-dependent and increases in low frequency range. In a magnetic tunneling system, thermal magnetization fluctuation in the magnetic layer can couple to the resistance through the spin-dependent tunneling effect and create low-frequency magnetic noise. In addition, the charge trapping effect in the oxide barrier may also contribute to the external low-frequency noise. Therefore, the depression of the noise in TMR magnetic field sensor, especially the low-frequency noise, is extremely important for the application with high resolution requirement. In this work, a low-frequency noise measurement system for TMR magnetic sensor is built by using a highaccuracy data acquisition card and a low noise preamplifier. After subtracting the circuit noise from the measured noise, the noise spectral patterns of TMR magnetic field sensor with a full Wheatstone bridge structure are obtained under various bias currents and external magnetic fields. It is found that the noise spectra of the TMR sensor exhibit a clear 1/f character in the low frequency region and the noise power spectral intensity is proportional to the square of the bias current. By fitting the power spectral density of the noise versus frequency in the TMR sensor, the Hooge parameters are obtained, which remain unchanged in the measurement. The noise intensity increases abruptly in the magnetization switching region of the free layer in magnetic tunnel junction, suggesting that the 1/f noise mostly comes from the magnetic noise. In a magnetic hysteresis loop, this noise power is strongly field-dependent, which is due to thermal magnetization fluctuations in magnetic layers. We attribute this magnetic fluctuation to thermally excited hopping of the magnetic domain wall between the pinning sites. Finally, according to the R-H transfer curves and the measured noise spectra of the TMR sensor, the detectable minimum magnetic fields of the sensor are 9 nT and 1.3 nT at 100 Hz and 4 kHz with 1 V input voltage, respectively. These results pave a way for optimizing the noise properties of TMR magnetic sensors.