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Model averaging has become a crucial statistical methodology, especially in situations where numerous models vie to elucidate a phenomenon. Over the past two decades, there has been substantial advancement in the theory of model averaging. However, a gap remains in the field regarding model averaging in the presence of missing censoring indicators. Therefore, in this paper, we present a new model-averaging method for accelerated failure time models with right censored data when censoring indicators are missing. The model-averaging weights are determined by minimizing the Mallows criterion. Under mild conditions, the calculated weights exhibit asymptotic optimality, leading to the model-averaging estimator achieving the lowest squared error asymptotically. Monte Carlo simulations demonstrate that the method proposed in this paper has lower mean squared errors compared to other model-selection and model-averaging methods. Finally, we conducted an empirical analysis using the real-world Acute Myeloid Leukemia (AML) dataset. The results of the empirical analysis demonstrate that the method proposed in this paper outperforms existing approaches in terms of predictive performance. [ABSTRACT FROM AUTHOR]