In this paper, we propose estimation-based elimination strategy, which improves sample efficiency of NeuroEvolution (NE) algorithms. The fitness of new individuals was estimated using fitness of individuals evaluated in the past generations. The estimation was achieved by taking average fitness of individuals with high correlation with the new individual. Estimation-based elimination strategy avoids evaluating individuals with low estimated fitness. We adapt estimation-based elimination strategy for state-of-the-art NE algorithms: CMA-NeuroES and CMA-TWEANN. From the experimental results of pole-balancing benchmark tasks, we show that the proposed strategy improves sample efficiency of the NE algorithms.