This paper addresses estimating the frequency of a cisoid in the presence of white Gaussian noise, which has numerous applications in communications, radar, sonar, and instrumentation and measurement. Due to the nonlinear nature of the frequency estimation problem, there is threshold effect, that is, large error estimates or outliers will occur at sufficiently low signal-to-noise ratio (SNR) conditions. Utilizing the ideas of averaging to increase SNR and weighted linear prediction, an optimal frequency estimator with smaller threshold SNR is developed. Computer simulations are included to compare its mean square error performance with that of the maximum likelihood (ML) estimator, improved weighted phase averager, generalized weighted linear predictor, and single weighted sample correlator as well as Cramer-Rao lower bound. In particular, with smaller computational requirement, the proposed estimator can achieve the same threshold and estimation performance of the ML method.