Surface nuclear magnetic resonance (SNMR) with multi-turn small air-core coil sensor (ACS) has considerable potential for the detection of shallow soil water or oil. However, loss of the early free induced decay signal and the distortion of the recorded signal arising from the ACS, make it difficult to quantitatively evaluate hydrological information. To address this problem, we propose an early signal acquisition and correction method. A fast-switching unit is applied to acquire the early signal. And a correction method based on the mathematical model of the ACS is proposed. Finally, the performance of the proposed method is evaluated by simulation experiments. Results show that the proposed method overcomes the signal attenuation caused by the ACS, while the fitting error of key parameters decreases from about 15% to 2%. Comparative test results of the existing method in an electromagnetically shielded laboratory further demonstrate the effectiveness of the proposed method.