Abstract: Faster-than-Nyquist (FTN) signaling is a kind of signal modulation technique, which is based on the compression in time domain and could achieve higher transmission rate and bandwidth efficiency. However, it would introduce infinite inter-symbol interferences (ISIs), which would bring a new challenge for carrier frequency offset estimation. The performance of traditional estimators would reduce in FTN signaling system. In this paper, the gradient descent algorithm would be applied to carrier frequency offset estimation. Without the aid of extra pilot, the unbiased estimation can be obtained by multiple iterative searches. Numerical simulation results indicate that gradient descent estimator has better performance than traditional estimators. Although it needs multiple iterations and more calculation, it could adapt to the characteristic of FTN signal better. The performance of decent gradient estimator is closer to Cramer-Rao bound (CRB), and it also has a good stability in all frequency offset regions.