Many exposures investigated in epidemiological case-control studies may vary over time. The effects of these exposures are usually estimated using logistic regression, which does not directly account for changes in covariate values over time within individuals. By contrast, the Cox model with time-dependent covariates directly accounts for these changes over time. However, the over-sampling of cases in case-control studies, relative to controls, requires manipulating the risk sets in the Cox partial likelihood. A previous study showed that simple inclusion or exclusion of future cases in each risk set induces an under- or over-estimation bias in the regression parameters, respectively. We investigate the performance of a weighted Cox model that weights subjects according to age-conditional probabilities of developing the disease of interest in the source population. In a simulation study, the lifetime experience of a source population is first generated and a case-control study is then simulated within each population. Different characteristics of exposure are generated, including time-varying intensity. The results show that the estimates from the weighted Cox model are much less biased than the Cox models that simply include or exclude future cases, and are superior to logistic regression estimates in terms of bias and mean-squared error. An application to frequency-matched population-based case-control data on lung cancer illustrates similar differences in the estimated effects of different smoking variables. The investigated weighted Cox model is a potential alternative method to analyse matched or unmatched population-based case-control studies with time-dependent exposures.