Estimating the false discovery rate (FDR) is one of the key steps in ensuring appropriate error control in the analysis of shotgun proteomics data. Traditional estimation methods typically rely on decoy sequence databases or spectral libraries, which may not always provide satisfactory results due to limitations of decoy construction methods. This study introduces the query mix-max (QMM) method, a decoy-free alternative for FDR estimation in proteomics. The QMM framework builds upon the existing mix-max procedure but replaces decoy matches with entrapment queries to estimate the number of false positive discoveries. Through simulations and real data set analyses, the QMM method was demonstrated to provide reasonably accurate FDR estimation across various scenarios, particularly when smaller sample-to-entrapment spectra ratios were achieved. The QMM method tends to be conservatively biased, particularly at higher FDR values, which can ensure stringent FDR control. While flexible, the protocol's effectiveness may vary depending on the evolutionary distance between the sample and entrapment organisms. It also requires a sufficient number of entrapment queries to provide stable FDR estimates, especially for low FDR values. Despite these limitations, the QMM method is a promising alternative as one of the first query-based FDR estimation approaches in shotgun proteomics.