Many crime datasets often display an excess of “1” counts, arises when arrested criminals have the desire and ability to avoid subsequent arrests. In this study, a new Horvitz–Thompson (HT) estimator under one-inflated positive Poisson–Lindley (OIPPL) distribution which allow for one-inflation and the existence of heterogeneity in the data is developed to estimate the hidden population size of criminals. From the simulation study and applications to real crime datasets, the OIPPL is capable to provide an adequate fit to the datasets considered and the proposed HT estimator is found to produce a more precise estimate of the population size with a narrower 95% confidence interval as compared to several other contending estimators considered in this study.