It is well known that the sample variance of a tally mean in Monte Carlo (MC) eigenvalue calculations is biased because of the intercycle correlations of the fission source distribution (FSD). This paper proposes the history-based batch method as a new method that can eliminate the dependency between samples and thereby estimate the real variance of the mean of the MC tally directly from routine cycle-by-cycle MC eigenvalue calculations. The new method estimates the real variance of the MC tally by the sample variance from tally estimates of the history-based batch defined as a set of histories with the same ancestor fission neutrons determined at the first active cycle MC run. The batch averages of the MC tally necessary for this estimate are obtained by correcting the individual tallies with the batch specific weight factors that are derived from independent FSD normalization of each individual batch. Diagnostic methods are also devised for small-batch-size problems, which one may encounter in applying the history-based batch method. The effectiveness of the history-based batch method is examined as a function of the dominance ratio and the batch size for the weakly coupled fissile array problems in comparison with those of bias estimation methods currently available. Its validity is also investigated in terms of the fuel storage facility problem exhibiting a slow source convergence.