Abstract: Abundance or population size is an important indicator for measuring biodiversity and has significant implications for ecological research. Based capture-recapture data without covariates, classic population size estimation methods include Chapman’s estimator and Dang et al.’s (2021) estimator, which are only applicable to the case of two captures. Their corresponding intervals are all Wald type, their coverage may be lower than confidence level, and may contain unreasonable values. To this end, we propose a likelihood estimation method for population size based on the full likelihood function. Compared to classical methods, a significant advantage of our method is that it is suitable not only for situations with two captures, but also for scenarios with multiple captures. Based on capture-recapture data without covariates, we constructed the global likelihood function and likelihood ratio statistics. We prove that the likelihood ratio statistic asymptotically follows a chi-square distribution with one degree of freedom, based on which we obtain the maximum likelihood estimator and likelihood ratio interval estimator for population size. Our numerical simulation results indicate that, unlike classical estimation methods, the coverage of our likelihood ratio confidence interval is always close to or higher than the confidence level. Our method still performs satisfactorily even when the number of captures exceeds 2, where Chapman’s estimator and Dang et al.’s (2021) estimator fails to work. Finally, through an analysis of the Hong Kong yellow bellied prinia data, we find that the left endpoint of the classic Wald type interval may be lower than the observed number of individuals, which is unreasonable. In contrast, our likelihood ratio interval always provides reasonable results, which demonstrates the widespread applicability and superiority of our likelihood ratio interval estimator.