One of the most important needs for wildlife managers is an accurate estimate of population size. Yet, for many species, including most marine species and large mammals, accurate and precise estimation of numbers is one of the most difficult of all research challenges. Open-population capture-recapture models have proven useful in many situations to estimate survival probabilities but typically have not been used to estimate population size. We show that open-population models can be used to estimate population size by developing a Horvitz-Thompson-type estimate of population size and an estimator of its variance. Our population size estimate keys on the probability of capture at each trap occasion and therefore is quite general and can be made a function of external covariates measured during the study. Here we define the estimator and investigate its bias, variance, and variance estimator via computer simulation. Computer simulations make extensive use of real data taken from a study of polar bears (Ursus maritimus) in the Beaufort Sea. The population size estimator is shown to be useful because it was negligibly biased in all situations studied. The variance estimator is shown to be useful in all situations, but caution is warranted in cases of extreme capture heterogeneity.