This paper proposes an estimation method to acquire the driver steering torque for the driver-automation co-driving vehicles considering sampling delay. Firstly, a vehicle lateral dynamics model is established with two steering inputs from both the driver and control system. The nonlinearities are described by a fuzzy method. Secondly, a fast adaptive observer is constructed to estimate the driver steering input while achieving the simultaneous estimation of vehicle lateral dynamics. Then, a set of matrix equalities is derived to ensure the asymptotic stability and minimize the estimation error with consideration of the sampling delay. Moreover, the observer gains are calculated by solving a condition. Finally, the effectiveness of the observer is verified via simulations.