The torque feedback of the vehicle's steering wheel or driver perception of the steering wheel is one of the aspects of steering quality that has been investigated extensively in recent decades. In this paper, the driver model for sensing torque feedback or haptic interaction between the vehicle equipped with a steer-by-wire system (SWB) and the driver has been designed. The driver model consists of a preview model and a neuromuscular model. The preview driver model calculates the desired angle of the steering wheel to follow the path, and the neuromuscular driver model that can perceive real-time torque feedback determines the real angle of the steering wheel according to muscular system transfer functions to follow its desired angle. Calculating of torques on the steering wheel requires estimation of the tire-road forces. Whereas directly calculating the tire-road forces is too difficult, particularly in the lateral vehicle dynamics, suitable estimator to estimate these forces designed. The simulation results using the Carsim and Simulink software indicate that the driver model performance improved 63 % when torque feedback is enabled. So the designed driver model with torque feedback has an important role in controlling and vehicle steering in conducting double lane-change maneuvers.