Vehicle automation is a fundamental approach to reduce traffic accidents and driver workload. However, there is a notable risk of pushing human drivers out of the control loop before automation technology fully matures. Cooperative driving (or vehicle co-piloting) is a novel paradigm which is defined as the vehicle being jointly navigated by a human driver and an automatic controller through shared control technology. Indirect shared control is an emerging shared control method, which is able to realize cooperative driving through input complementation instead of haptic guidance. In this paper we first establish an indirect shared control method, in which the driver’s commanded input and the controller’s desired input are balanced with a weighted summation. Thereafter, we propose a predictive model to capture driver adaptation and trust in indirect shared control. In this model, adaptation is interpreted as drivers integrating the controller’s input transformation strategy into their predictor, and trust is modeled as a change of their cost function. Lastly, we perform simulations in a standard double lane change maneuver to evaluate the effects of driver adaptation and trust on the indirect shared control performance. The major findings of this study include: 1) Driver adaptation and trust are directly related to the control effort, but do not significantly affect the vehicle stability because the driver’s steering input is filtered by the controller; 2) Driver’s control effort is more sensitive to the trust level, with the simulation results showing that distrust would largely increase the driver’s steering effort even if he has well adapted to the controller; 3) A system failure (the controller suddenly hands over the control authority to the driver without notification) would endanger the vehicle because the driver cannot switch back his internal model and adjust his control objectives immediately.