Based on the least square (LS) approximation of sinusoidal signal in frequency domain by sample data, a frequency estimator is derived. Since sinusoidal signals are narrow-banded whereas white noise spreads equally in the whole spectrum, only narrow-band approximation around the actual tone is needed, and thus the influence of noise can be decreased significantly with high computational efficiency. Experimental results show that, without any iterations, the performance of the proposed estimator is close to the Cramer-Rao Bound (CRB), and has a lower SNR threshold compared with other existing estimators.