<p>The present paper puts forward a novel and unconditionally stable numerical approach for valuing American options (AO) on zero-coupon bonds (ZCBs), considering the framework of the Hull-White (HW) model. By integrating a front-fixing (FF) transformation with the implicit finite difference (IFD) technique, the method facilitates the simultaneous determination of optimal exercise boundaries and option prices, effectively reformulating the problem of the original free boundary into a bounded one. Additionally, the proposed approach has demonstrated unconditional stability across all grid ratios, ensuring robustness for any step sizes. To enhance the reliability of the obtained results, numerical experiments are conducted to illustrate the efficiency and feasibility of the suggested approach. This study includes comparisons with existing approaches for solving the AO on zero-coupon bonds to affirm the numerical findings and show the effectiveness of the employed approach.</p>