A semiparametric estimation procedure is proposed to model capture-recapture data with the aim of estimating the population size for a closed population. Individuals' covariates are possibly time dependent and missing at noncaptured times and may be measured with error. A set of estimating equations (EEs) based on covariate process and capture-recapture data is constructed to estimate the relevant parameters and the population size. These EEs can be solved by an algorithm similar to an EM algorithm. Simulation results show that the proposed procedures work better than the naive estimate. In some cases they are even better than "ideal" estimates, for which the true values of covariates are available for all captured subjects over the entire experimental period. We apply the method to a capture-recapture experiment on the bird species Prinia flaviventris in Hong Kong.