Equations for the effective size (Ne) of a population were derived in terms of the frequencies of a pair of offspring taken at random from the population being sibs sharing the same one or two parents. Based on these equations, a novel method (called sibship assignment method) was proposed to infer Ne from the sibship frequencies estimated from a sibship assignment analysis, using the multilocus genotypes of a sample of offspring taken at random from a single cohort in a population. Comparative analyses of extensive simulated data and some empirical data clearly demonstrated that the sibship assignment method is much more accurate [measured by the root mean squared error, RMSE, of 1/(2Ne)] than other methods such as the heterozygote excess method, the linkage disequilibrium method, and the temporal method. The RMSE of 1/(2Ne) from the sibship assignment method is typically a small fraction of that from other methods. The new method is also more general and flexible than other methods. It can be applied to populations with nonoverlapping generations of both diploid and haplodiploid species under random or nonrandom mating, using either codominant or dominant markers. It can also be applied to the estimation of Ne for a subpopulation with immigration. With some modification, it could be applied to monoecious diploid populations with self-fertilization, and to populations with overlapping generations.