The magnetic resonance sounding (MRS) technique is a non-invasive geophysical method that can provide unique insights into the hydrological properties of groundwater. The Cu coil sensor is the preferred choice for detecting the weak MRS signal because of its high sensitivity, low fabrication complexity and low cost. The tuned configuration was traditionally used for the MRS coil sensor design because of its high sensitivity and narrowband filtering. However, its narrow bandwidth may distort the MRS signals. To address this issue, a non-tuned design exhibiting a broad bandwidth has emerged recently, however, the sensitivity decreases as the bandwidth increases. Moreover, the effect of the MRS applications is often seriously influenced by power harmonic noises in the developed areas, especially low-frequency harmonics, resulting in saturation of the coil sensor, regardless of the tuned or non-tuned configuration. To solve the two aforementioned problems, we propose a matching network consisting of an LC broadband filter in parallel with a matching capacitor and provide a design for a coil sensor with a matching network (CSMN). The theoretical parameter calculations and the equivalent schematic of the CSMN with noise sources are investigated, and the sensitivity of the CSMN is evaluated by the Allan variance and the signal-to-noise ratio (SNR). Correspondingly, we constructed the CSMN with a 3 dB bandwidth, passband gain, normalized equivalent input noise and sensitivity (detection limit) of 1030 Hz, 4.6 dB, 1.78 nV/(Hz)1/2 @ 2 kHz and 3 nV, respectively. Experimental tests in the laboratory show that the CSMN can not only improve the sensitivity, but also inhibit the signal distortion by suppressing power harmonic noises in the strong electromagnetic interference environment. Finally, a field experiment is performed with the CSMN to show a valid measurement of the signals of an MRS instrument system.