An improved class of estimators for population mean using one auxiliary character in the presence of non-response has been suggested and its properties are studied for the fixed sample sizes (n′, n), for the fixed cost and for the specified precision. The proposed class of estimators is found to be more efficient than the relevant estimators for the fixed sample sizes (n′, n) and for the fixed cost C ≤ C0, which is supported with the help of an empirical study. The proposed class of estimators is also having less cost than the cost incurred in the relevant estimators for the specified precision which is also supported by empirical study.