This study proposes a novel method for estimating driveline torques for a vehicle with a dual-clutch transmission (DCT). Knowledge of the driveline torque states, such as the torque transmitted through a clutch, and transmission output torque, allows a significant improvement in powertrain control performance, especially during gear shifts and vehicle launch. Furthermore, vehicles with DCT or automatic transmission whose gear shift processes involve clutch-to-clutch shifts require information about the individual clutch torques for sophisticated torque transfer control. Thus, an adaptive torque observer, which is applicable to DCT drivelines, is developed to estimate the torque transmitted through each clutch and output shaft simultaneously. In order to overcome the lack of measurements in a production car, the proposed observer uses multiple adaptation laws in accordance with driving conditions so that it treats parameter uncertainties effectively, such as those of the clutch friction coefficient, nominal engine torque as well as vehicle load torque. Also, the observer is characterized by its simple and intuitive structure based on a reduced-order driveline model. The estimation performance of the observer including its robustness to the parameter errors is evaluated not only by simulations but also by experiments under various driving scenarios.