Assessing and monitoring genetic diversity is vital for understanding the ecology and evolution of natural populations but is often challenging in animal and plant species due to technically and physically demanding tissue sampling. Although environmental DNA (eDNA) metabarcoding is a promising alternative to the traditional population genetic monitoring based on biological samples, its practical application remains challenging due to spurious sequences present in the amplicon data, even after data processing with the existing sequence filtering and denoising (error correction) methods. Here we developed a novel amplicon filtering approach that can effectively eliminate such spurious amplicon sequence variants (ASVs) in eDNA metabarcoding data. A simple simulation of eDNA metabarcoding processes was performed to understand the patterns of read count (abundance) distributions of true ASVs and their polymerase chain reaction (PCR)-generated artifacts (i.e., false-positive ASVs). Based on the simulation results, the approach was developed to estimate the abundance distributions of true and false-positive ASVs using Gaussian mixture models and to determine a statistically based threshold between them. The developed approach was implemented as an R package, gmmDenoise, and evaluated using single-species eDNA metabarcoding datasets in which all or some true ASVs (i.e., haplotypes) were known. Example analyses using community (multi-species) eDNA datasets were also performed to demonstrate how gmmDenoise can be used to derive reliable intraspecific diversity estimates and population genetic inferences from noisy amplicon sequencing data. The gmmDenoise package is freely available in the GitHub repository (https://github.com/YSKoseki/gmmDenoise).