In a regression analysis, it may happen that variables are not measured precisely. When the covariates are measured with measurement errors, the estimation in regression parameters will be biased in usual. However, for the capture-recapture experiments, the investigations into the effect of measurement errors have been very limited. Besides the approaches of regression calibration and conditional score that proposed by Hwang and Huang (2003, 2005), the present paper disscusses an approximate estimation through Taylor expansion for the discrete time capture-recapture experiment. As a result, we find that the small measurement error approximation is a convenient and efficient way for estimaing both in regression parameters and in the population size. Simulation results are also provided for different distributions of measurement error and covariate.