Abstract: Nuclear quadrupole resonance (NQR) is a solid-state radio frequency (RF) spectroscopic technique, allowing the detection of many high explosives. Unfortunately, NQR signals are inherently weak and vulnerable both to the thermal noise of the coil and any external radio frequency interference (RFI), the practical use of NQR is restricted by the low signal-to-noise ratio (SNR). On the basis of the investigation of the characteristic of the free induction decay (FID) signal, the linear prediction estimator based on the total least squares is applied to estimate the parameters of the NQR. The effectiveness of this algorithm is demonstrated with the results of both simulated data and experimental data.