We introduce an estimator for an unknown population size in a capture–recapture framework where the count of identifications follows a geometric distribution. This can be thought of as a Poisson count adjusted for exponentially distributed heterogeneity. As a result, a new Turing-type estimator under the geometric distribution is obtained. This estimator can be used in many real life situations of capture–recapture, in which the geometric distribution is more appropriate than the Poisson. The proposed estimator shows a behavior comparable to the maximum likelihood one, on both simulated and real data. Its asymptotic variance is obtained by applying a conditional technique and its empirical behavior is investigated through a large-scale simulation study. Comparisons with other well-established estimators are provided. Empirical applications, in which the population size is known, are also included to further corroborate the simulation results.