A unified likelihood-based approach is proposed to estimate population size for a continuous-time closed capture-recapture experiment with frailty. The frailty model allows the capture intensity to vary with individual heterogeneity, time, and behavioral response. The individual heterogeneity effect is modeled as being gamma distributed. The first-capture and recapture intensities are assumed to be in constant proportion but may otherwise vary arbitrarily through time. The approach is also extended to capture-recapture experiments with possible random removals. Simulation studies are conducted to examine the performance of the proposed estimators. By asymptotic efficiency comparison and simulation studies, the proposed estimators have been shown to be superior to their discrete-time model counterparts in genuine continuous-time capture-recapture experiments.