In capture-recapture studies, capture probabilities would depend on both individuals covariates and the decreasing number of available traps during the experiment. In this paper, we examine a proportional trapping model with the use of individuals covariates in modelling the heterogeneity. We use the martingale estimating equation to obtain an estimator for the population size. It is proved to be asymptotically normal. Simulations and a real example are used to assess the performance of the proposed estimator.