In this study, we propose two estimation methods for considered marginal models under the cluster data setting with informative cluster size. The information of within-cluster correlation is appropriately used through the minimum cluster size in our approach, which is not fully considered in the within-cluster resampling (WCR) and cluster-weighted generalized estimating equation (CWGEE) methods. It is known in the former works that the approaches of WCR and CWGEE are asymptotically equivalent but the WCR estimation procedure is computationally intensive. When the within-cluster correlation is available and the minimum cluster size is greater than one, our estimatiors improve the inefficiency of the both estimators. The finite sample properties of the proposed estimators are examined through a Monte Carlo simulation. Meanwhile, a comparison with the CWGEE method is made in the numerical study.