Existing F-statistic estimators fail to account for any genetic correlations among individuals or subpopulations and assume that all samples are independent. This may result in inaccurate F-statistic estimations for natural populations. Here, we derive the expectations of previous F-statistics estimates using extended kinship coefficients. On this basis, we developed a new method for F-statistic estimation that accounts for non-independence of samples, finite sample sizes, and autopolyploidy. As proof of principle, using the same simulated datasets we compared the accuracy of several established F-statistic estimators with our new estimator. We found that our new method outperformed all of the other methods we used and showed almost no bias. Our new method has been added as a new function to our existing software package polygene V1.4, which is freely available at http://github.com/huangkang1987/polygene.